Laurence Hastings, earl of Pembroke, was born in Allesley, Warwickshire either on 20 March 1320 or 20 March 1321. His proof of age says that he was born on "the feast of St Cuthbert, 14 Edward II", which is 20 March 1321 (Edward II's fourteenth regnal year ran from 8 July 1320 to 7 July 1321), but confusingly, the proof was taken in May 1341 and says that Laurence was then "21 years of age and more". Edward III allowed Laurence to take possession of his late father's inheritance, because he had proved his age and sworn homage, on 24 May 1341. So most probably, the jurors who took part in the proof of age erred on Edward II's regnal year and meant to say that Laurence was born on 20 March 1320, i.e. the feast of St Cuthbert, 13 Edward II. Because things are rarely as straightforward in medieval inquisitions post mortem and proofs of age as you'd hope, an inquisition in Bedfordshire on 23 April 1325 stated that Laurence Hastings was "aged 6 about the feast of the Annunciation last", which gives a date of birth of c. 25 March 1319, not 1320. Inquisitions in Shropshire and Monmouth in July 1325, however, said that Laurence was "aged 5 on the feast of St Cuthbert last".  Given Laurence's unusual first name, which doesn't appear previously in the Hastings family (and the feast of St Laurence is 10 August, not in March), I assume he was named after a godfather. Pity his parents didn't call him Cuthbert.
Laurence was the sole heir of his mother Juliana Leyb(o)urne (1303/4-67), a landowner in Kent and countess of Huntingdon by her third marriage, though, in the end, Juliana outlived her son by nearly twenty years; the sole heir of his father John, Lord Hastings (1286-1325) and his grandfather John, Lord Hastings (1262-1313); and the co-heir, with his father's cousins Joan and Elizabeth Comyn, of his great-uncle Aymer de Valence, earl of Pembroke (d. 1324). Laurence was betrothed in 1325, aged five, to Hugh Despenser the Younger's third daughter Eleanor, Edward II's great-niece, but Queen Isabella forced Eleanor into a nunnery a few weeks after Hugh's execution. In 1328 or 1329* Laurence married Agnes, one of the eight daughters of Roger Mortimer and Joan Geneville, first earl and countess of March, instead. Their only son and Laurence's heir, John Hastings, earl of Pembroke, was born in Sutton Valence, Kent on 29 August 1347, and his godparents were William, prior of Leeds in Kent, Sir John Pulteney (d. 1349), former mayor of London, and Maud Say. Laurence died sometime between 28 and 31 August 1348 when his son was exactly a year old, and the boy became a royal ward. John Hastings married firstly Edward III and Queen Philippa's fifth and youngest daughter Margaret of Windsor (b. 20 July 1346), who died in the early 1360s most probably before the couple were old enough to consummate the marriage, and secondly, Anne Manny or Mauny (b. c. 24 July 1354), co-heir of her mother Margaret, countess of Norfolk, and a great-granddaughter of Edward I. John and Anne's only child and heir, another John Hastings, was born on c. 11 November 1372. 
* Chronicler Adam Murimuth states that Laurence and Agnes married in late May or early June 1328, but as Roger Mortimer's biographer Ian Mortimer points out in his Greatest Traitor (pp. 294, 323), it is perhaps unlikely that Agnes would have married such a great heir as Laurence Hastings before Roger himself became an earl in October 1328. Inquisitions taken in Kent, Berkshire and Herefordshire in 1349 state that Laurence married Agnes Mortimer "in his seventh year", though this also seems too early.  At any rate, Laurence and Agnes married when they were both still children, most probably in 1329. Agnes's date of birth and her place in the birth order of Roger Mortimer and Joan Geneville's many children are unknown, but it is unlikely that she was much older than Laurence, and might have been selected as his bride because she was the Mortimer daughter closest to his age. The same applies to Laurence's first fiancée, Hugh Despenser and Eleanor de Clare's third daughter Eleanor Despenser: she was raised with Edward II and Queen Isabella's daughters Eleanor of Woodstock (b. 1318) and Joan of the Tower (b. 1321), implying that she was of similar age to them and to Laurence Hastings. Roger Mortimer was granted Laurence's marriage, presumably by Queen Isabella, on 17 February 1327. 
Sometime around 9 or 12 March 1349 a few months after Earl Laurence died, a man named Sir William Hastings died as well, perhaps of the plague which was then raging in England. William's inquisition post mortem and various entries in the chancery rolls state that he was 1) illegitimate ("he has no heir because he was a bastard") and 2) Laurence's brother. Helen Matthews' The Legitimacy of Bastards: The Place of Illegitimate Children in Later Medieval England (2019) claims that William was Laurence's illegitimate son. Laurence, however, was himself only born in 1320 and was only 28 when he died in 1348, so was far too young to have fathered a son who was old enough to be a knight and a landowner by the time of his death in 1349. An inquisition held in Abergavenny in early 1354 states outright that William was Laurence's brother ("...giving the values at the time of the deaths of the said earl and William de Hastings, his brother, and at the present time").  On 2 September 1348 just days after Laurence died, the following entry appears on the Fine Roll: "Grant to William de Hastynges, brother of Laurence de Hastynges, earl of Pembroke, and Robert de Elford, executors of the will...".  A petition Laurence sent to Pope Clement VI, which Clement only granted in June 1349 a few months after Laurence's death, also confirms the two men's relationship: "Laurence de Hastings, earl of Pembroke. For plenary remission to himself, his wife, William de Hastings his brother, and John de Reygate, knights...". 
William's identity is, therefore, beyond all doubt: he was a brother of Laurence, earl of Pembroke, he was a "bastard", and he used the name Hastings, and therefore he must have been an illegitimate son of Laurence's father John, Lord Hastings. There is much evidence that Laurence was on excellent terms with and extremely close to his illegitimate half-brother, and after Laurence turned 21 in the early 1340s and came into his inheritance, he gave William several of his manors in Kent, Berkshire, Surrey, Herefordshire and Wales, for William to hold for the rest of his life when they would revert to Laurence and his rightful heirs. William's IPM duly stated that the heir to the manors he had held from Laurence was Laurence's son John, who turned two years old in August 1349. In one of the manors William had held, Paddington ('Padingden'), it was stated on 16 April 1349 that all his tenants there "are now dead, except ten" - a horrifying example of the awful reality of the Black Death. 
Laurence's father John, Lord Hastings, born c. 29 September 1286, was seventeen or eighteen years older than his wife Juliana Leybourne - she was said to be three years old in July/September 1307 and six in March/April 1310 - and had to wait a long time until she was old enough to consummate their marriage.  The date of their wedding is not recorded, though there's a reference to "John de Hastinges and Juliana his wife" on 8 June 1319, and on 3 April 1319 Edward II referred to a previous grant of four manors which Juliana's grandmother, Juliana Leybourne the elder, had made to John Hastings.  Juliana was still only fifteen, perhaps recently sixteen, when she gave birth to Laurence in March 1320, and had no more children with any of her three husbands; perhaps Laurence's birth was a difficult one. Given her youth, it's not really surprising to learn that John Hastings had a relationship with another woman that resulted in a child, assuming that William Hastings was conceived and born in the period when Juliana Leybourne was too young to sleep with her husband. John died on 20 January 1325, aged thirty-eight, two months before his son's fifth birthday.
John, Lord Hastings apparently named his illegitimate son after his older brother William Hastings, who was born in October 1282 and for many years was the Hastings heir, but died not long before 1 March 1311 leaving no children from his marriage to Eleanor Martin, two years before his and John's father John the elder died in February 1313.  The inquisition post mortem of the illegitimate Sir William Hastings in 1349 calls him William de Hastynges le neveu, 'the nephew', presumably to differentiate him from the long-dead William Hastings (d. 1311), his uncle. Confusingly, an entry on the Close Roll assigning dower lands to Agnes Mortimer as the widow of Laurence Hastings in July 1349 calls William both le neveu and le frere, 'the brother'.  Presumably, this means nephew of William Hastings (d. 1311) and brother of Laurence, the late earl of Pembroke. On 3 September 1348 six months before he died, the illegitimate Sir William Hastings was one of two people who acknowledged a debt of 400 marks to Laurence Hastings' stepfather William Clinton, earl of Huntingdon (d. 1354), Juliana's third husband; the other man was Laurence's co-executor Robert El(le)ford.  The 3rd of September 1348 was just days after Laurence died.
Again confusingly, a grant in May 1345 by Laurence Hastings to his mother Juliana Leybourne and stepfather William Clinton talks of "Alice late the wife of William de Hastynges, Laurence's uncle."  As the illegitimate Sir William Hastings was still alive, this Alice can't have been his widow as the wording indicates, so this must mean the legitimate William Hastings who died in 1311 and was indeed Laurence's uncle. This William's widow was in fact named Eleanor, née Martin, and she died in December 1342 after outliving her husband for more than thirty years. It would seem therefore that 'Alice' was an error for Eleanor Hastings née Martin. I can't see any evidence that the illegitimate Sir William Hastings ever married, and his inquisition post mortem states that he died without an heir of his body.
As for Laurence's widow Agnes Mortimer, she married her second husband John Hakelut or Haclut sometime before 12 November 1351; on 28 October 1348, he had been one of the three attorneys she appointed to receive her Hastings dower lands. Edward III exempted John Hakelut "from knighthood, for life" in May 1342. On 1 March 1354, Edward ordered an investigation into the "very many damages, grievances, injuries, extortions and oppressions" which the couple and their officials had committed in eleven manors in the Welsh lordship of Abergavenny "which came into his [the king's] hands as escheats by the death of William de Hastynges" and were part of the inheritance of Agnes's then six-year-old son John Hastings.  John Hakelut died before 12 February 1357, and Agnes died on 25 July 1368, a few weeks before her son turned twenty-one. She had dictated her will at her house in London on 10 October 1367 requesting burial at the Minoresses' house in the city, and left a suit of green cloth of gold to the Priory of Abergavenny, "where my lord [Laurence Hastings] lies buried".  Laurence's father John was also buried there in 1325, and his wooden effigy can still be seen today. Agnes's will mentions her daughter Joan, to whom she left "the benefit of the marriage of Ralph de Greystoke, and a bed with her father's arms". I'm not sure whether Joan's father was Laurence Hastings, earl of Pembroke, or John Hakelut, and if anyone does know, please tell me. Agnes can't have been much more than about thirty-two, thirty-three or so when she wed Hakelut in c. 1351 and might only have been in her late twenties, so was certainly still young enough to have another child. She probably named her daughter after her mother Joan Geneville, dowager countess of March (d. 1356), and her will referred to "John de Hastings, my son" and "Joan, my daughter" without a last name, which perhaps indicates that Joan was John Hakelut's daughter.
1) Calendar of Inquisitions Post Mortem 1317-27, no. 612; CIPM 1336-46, no. 337; Calendar of Close Rolls 1341-3, p. 95; Calendar of Fine Rolls 1337-47, p. 117.
2) CIPM 1347-52, no. 118; CIPM 1365-9, no. 266; CIPM 1370-3, no. 148; CIPM 1374-7, no. 148; CIPM 1384-92, nos. 11-31.
3) CIPM 1347-52, no. 287.
4) Calendar of Patent Rolls 1327-30, p. 22.
5) CIPM 1347-52, nos. 118, 287, 497; CFR 1347-56, pp. 113, 330, 352, 354; CCR 1349-54, p. 550; Calendar of Inquisitions Miscellaneous 1348-77, no. 78.
6) CFR 1347-56, p. 95.
7) Petitions to the Pope 1342-1419, p. 162.
8) CIPM 1347-52, nos. 118, 287, 497; CPR 1340-3, p. 515; CPR 1348-50, pp. 191, 274; CPR 1350-4, p. 329; CPR 1354-8, p. 58; CCR 1349-54, pp. 28, 40.
9) CIPM 1300-07, no. 410; CIPM 1307-17, nos. 220, 412.
10) CPR 1317-21, pp. 324, 375.
11) CFR 1307-19, p. 83.
12) CFR 1347-56, p. 118; CCR 1349-54, p. 40.
13) CCR 1346-9, p. 587.
14) CCR 1343-6, pp. 567-8.
15) CPR 1340-3, p. 426; CPR 1350-4, p. 199; CPR 1354-8, p. 58; CIPM 1347-52, no. 118.
16) CFR 1356-68, p. 33; CIPM 1365-9, no. 226; Testamenta Vetusta, vol. 1, pp. 71-2.