He married (1st) in 1362 (date of property settlement) Agnes ___.
1370 Marriage to Joan D'Oyley
He married (2nd) by settlement dated 1370 Joan D'Oyley, daughter of John d'Oyley, Knt, of Ronton, Staffordshire, Warnham, Sussex, Stoke Doyle, Northamptonshire, and Whatton, Leicestershire, b Margaret, daughter of Thomas de Tregoz, Knt, 2nd Lord Tregoz. She was born about 1344.
Additional Marriage Links
Some genealogies show him married to a Joan D'Oyley, born 1313 in Gretworth, Northamptonshire, either in addition to, or in place of, Joan, shown above. No documentation has been found for such a person.
He is shown in some genealogies as being married to Beatrice Hoo, b. Crecy, 1354, d. 1375. This is probably a reference to Sir Thomas Lewknor who is referenced as the father of one or more daughters named Beatrice,  but who himself has not been placed in relationship to other Lewknors. 
Sir Thomas de Lewknor died in 1375. His widow remarried.
Named by Richardson (2013)
Richardson reports no issue of the marriage of Thomas and Agnes and reports that Thomas and Joan had two sons, Roger and John, and one daughter, Katherine.
Roger, Esq, b. 1369 of Thomas and Joan and died before 15 Nov 1400. Believed by some to be the same as Sir Thomas Lewknor, b. 1362 of Thomas and Joan. Named in Stemmata which states, "Sir Thomas Lewknor, MP 1404, d. 1471. Called Sir Roger in Sussex Arch Soc iii p. 89. m. Elizabeth Carew.
John, b. 1371 of Thomas and Joan. Named in Stemmata which states, "John Lewknor, MP Sussex 1449, mar. Isabel, dau. of Sir Roger Covert.
Katherine. Named only by Richardson, not by other sources.
Named by Robertson (1893)
Robertson's 1893 work Stemmata names Thomas and John as children and adds Margaret to the list of known children.
Margaret Lewkenor, b. 1373 of Thomas and Joan, probably the same as Margaret Lewknor, b. 1373 of Thomas and unknown. Margaret was born about 1373. Margaret is the child of Thomas Lewknor and Joan D'Oyly. She married Sir John Covert. 
Not verified and not linked
Thomas Lewknor, b. 1362, father of Beatrice, is sometimes shown as the son of Thomas Lewknor and Beatrice Hoo, b. Crecy, 1354, d. 1375. This probably the same Sir Thomas Lewknor who is referenced as the father of one or more daughters named Beatrice,  but who himself has not been placed in relationship to other Lewknors.