His father was Thomas de Driby.

Paul Reed posted this to soc.gen.medieval in Jan 2002:

"FWIW:

" John de Driby (son of Thomas) and Amie de Gaveston had one surviving
daughter, Alice de Driby.  She married three times, first to Sir Robert
Touchet [no issue], second (as his second wife) to Sir Ralph Basset, Lord
Basset of Sapcote [b. ca. 1315, d. 17 July 1378]; and third, by 28 May
1379,  to Sir Anketil Mallory [CFR 1377-83, 9:135].  Hunt theorized
that Alice married a fourth time, to Sir William Papworth [TAG
40:97-8], but here again Hunt was wrong [Alice, wife of Sir William
Papworth (d. 4 Sep. 1414), survived him and died 7 July 1416 (CIPM
20:101 [no. 324], 165 [no. 524]; see TAG 40:97)].

"Alice had no surviving issue by her first husband.  By her second
husband, Alice had one daughter, Elizabeth Basset, born 1 Aug. 1372,
younger daughter and coheir of her father [CP 2:7-8; Elizabeth Basset
married Richard Grey, Lord Grey of Codnor, Admiral of the Fleet, K.G.
(CP 6:127-9)]. By Sir Anketil Mallory, of Kirkby Mallory, whom Alice
married about 1379, she had several children.  Sir Anketil Mallory died
26 Mar. 1393 [CIPM 17:82 (no. 179)], will dated 17 Aug. 1390 and proved
16 Apr. 1393 [Alfred Gibbons, Early Lincoln Wills… (Lincoln, 1888), 57].
His son and heir, Thomas, was aged twelve or more at his father’s death
[b. ca. 1380-1].  Thomas’s daughter and heir, Elizabeth, was heir to her
grandmother Alice (Driby) (Touchet) (Basset) Mallory, and married Sir
Robert Ever/Eure [d. 3 Feb. 1480], who held Breedon in her right.

"Alice died 12 Oct. 1412 [CIPM 19:372-4 (nos. 1031-5: lands in cos.
Derby, Leicester, Lincoln, Northampton, and Stafford)], leaving a will
dated 14 Apr. and  proved 26 Oct. 1412.  Her will included bequests for
the souls of her former husbands, Sir Ralph Basset, Sir Richard Tochet
and Sir Anketin Malores, and for her late parents, John Dryby and Amie his
wife.  She also named her daughter Elizabeth, wife of Lord Grey, daughter
Margery, wife of Sir Robert Moton, knight [MP], daughter Beatrice, wife
of Sir John Bagot, knight [MP], son William Maloree [father of Thomas,
whom some say is author of the Morte d’Arthur], Elizabeth, daughter of
[her son] Sir Thomas Maloree, knight, and Anne Bradley and her daughter
Beatrice [Gibbons, Lincoln Wills, 110-11].  Hunt erred yet again when
he deduced that Sir William Mallory was father of a daughter named
Margaret who married Sir Robert Corbet, of Moreton Corbet [TAG
35:104-5, 37:50, 40:98]. Sir William Mallory’s wife Margaret was
actually the widow of Sir Robert de Corbet."

"This was from “Proving' Illegitimacy: Amie, the
Daughter of the King's Favorite, Piers de Gaveston--
Not That of His Wife,” National Genealogical
Society Quarterly, 88:32-49 (March 2000)."
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Paul Reed also posted this on the Droby ancestry on 27th Feb 2001:

John de Driby of Tattershall was the third and youngest son of Robert de
Driby [d. ca. 1279] by Joan de Tattershall [d. 8 Oct. 1329]. Simon de
Driby, eldest son, died without issue in 1332, leaving his brother
Robert as his heir. Robert also died without issue, leaving John as heir
male, but on his death without issue in 1334 all lands that had not been
previously conveyed were inherited by his sister Alice de Driby [d.
1341], wife of William Bernake [d. 1339]. Aside from conveying Breedon
to John, son of Thomas de Driby, John de Driby of Tattershall conveyed
the castle of Tattershall with other manors and lands to Sir John de
Kirketon, who successfully held them to his death in 1367 [CIPM 12:127-8
(no. 150); CPR 1361-4, 519-20]. Incredibly, Hunt concluded that John was
not the youngest son, but Joan's eldest child, "probably born before her
marriage" [TAG 37:47, 50]. If John had been illegitimate, he could not
have inherited from his father or his mother. Also, Hunt at first
concluded that Amie's husband John was the legitimate son of this John
de Driby of Tattershall [TAG 37:47]. Then when it was discovered that
Amie's husband was son of Thomas de Driby, Hunt theorized that Thomas
was illegitimate son of this John, who was only called 'parson' in the
last two years of his life. Chronology suggests that Thomas was actually
about the same age as John, son of Joan (de Tattershall) de Driby [her
son John was probably born shortly before his father's death, ca.
1279/80]. As John of Tattershall's grandfather, an earlier Sir Simon de
Driby, had two brothers, Hugh and Ralph, who both qualified for
knighthood, and issue is known, there is no reason to conclude that
John's father Thomas was illegitimate.

John de Driby (son of Thomas) and Amie de Gaveston had one surviving
daughter, Alice de Driby. She married three times, first to Sir Robert
Touchet [no issue], second (as his second wife) to Sir Ralph Basset,
Lord Basset of Sapcote [b. ca. 1315, d. 17 July 1378]; and third, by 28
May 1379, to Sir Anketil Mallory [CFR 1377-83, 9:135]. Hunt theorized
that Alice married a fourth time, to Sir William Papworth [TAG 40:97-8],
but here again Hunt was wrong [Alice, wife of Sir William Papworth (d. 4
Sep. 1414), survived him and died 7 July 1416 (CIPM 20:101 [no. 324],
165 [no. 524]; see TAG 40:97)].

I am not aware that any other published article or book on this matter
narrowed down the marriage to Anketil de Mallory as occurring between 17
July 1378 [the death of Ralph Basset] and 28 May 1379. Paul
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