In answer to your question, the first seven generations of the descent from Sir Sampson Foliot down to Edward Carleton are as shown below. From Generation 7 forward, I'm sure you can make your connection to Edward Carleton. I believe the problem generation for you is Generation 5 below. All secondary sources I've consulted identify Margery, wife of Herbert de Saint Quintin, as a Lisle, which I believe is correct, but I'm not sure on what evidence this identification has been made. It surely comes from an earlier source which I haven't been able to locate. I can state with certainty that Margery de Lisle's husband, Sir Herbert de Saint Quintin, witnessed a deed of Margery's widowed mother Alice de Lisle and her brother, Henry le Tyeys, in 1346, as shown by a document copied below from the online Discovery catalogue. This deed is good supporting evidence for the published sources which identify Margery as a Lisle.
Best always, Douglas Richardson, Salt Lake City, Utah
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1. Sampson Foliot, Knt., living 30 May 1281, died before Easter term 1282, married Alice _____, living Easter term 1282.
2. Joan Foliot, married Henry le Tyeys, of Alverton (in Penzance), Cornwall, Albury, Fritwell, and Shirburn, Oxfordshire, etc., died by 1282.
3. Henry le Tyeys, Knt., 1st Lord Tyeys, married Hawise de Montagu.
4. Alice le Tyeys, married Warin de Lisle, Knt.
5. MARGERY DE LISLE, married HERBERT DE SAINT QUINTIN, Knt., of Brandesburton, Yorkshire, Great Bradley (in Cookham), Berkshire, Stanton St. Quintin, Wiltshire, Frome St. Quintin, Dorset, etc., son and heir of Herbert de Saint Quintin, of Stanton St. Quintin, Wiltshire, by Lora, daughter of Walter de Fauconberge, Lord Fauconberge. They had two daughters, Elizabeth and Lora. He witnessed a charter of Alice, widow of Warin de Lisle, Knt., and her son, Henry Tyeys, Knt. in 1346. SIR HERBERT DE SAINT QUINTIN died in May 1347. His widow, Margery, married (2nd) before 13 Feb. 1350/1 without license ROGER HUSEE (or HUSSEY), Knt., of West Betchworth, Surrey, Moreton, West Hemsworth, and Ringstead, Dorset, Barton Stacey, Hampshire, etc., son and heir of John Husee, Knt., of Moreton and West Hemsworth, Dorset, Bridmore (in Berwick St. John), Wiltshire, etc., by Maud, daughter of Reynold de Haselden. He was born at Moreton, Dorset 7 July 1305. They had no issue. He was on the king’s service in 1332. He was summoned for military service 24 Dec. 1334 and 27 March 1335. He was summoned to Parliament from 20 Nov. 1348, 1 Jan. 1348/9, and 10 March 1348/9, by writs directed Rogero Huse or Husee, whereby he is held to have become Lord Husee. His wife, Margery, died 21 May 1361. SIR ROGER HUSEE, Lord Husee, died 1 Sept. 1361. Kimber & Johnson, Baronetage of England 1 (1771): 431–437 (sub St. Quintin) (author identifies Margery, wife of Herbert de Saint Quintin, as “daughter and coheir of Warin d’Insula, Lord Lisle.”). Banks, Dormant & Extinct Baronage of England 1 (1807): 412–414 (sub St. Quintin) (author identifies Margery, wife of Herbert de Saint Quintin, as “daughter and coheir of Warine de Lisle”). Poulson, Hist. & Antiqs. of the Seigniory of Holderness 1 (1840): 267 (author identifies Margery, wife of Herbert de Saint Quintin, as “daughter and co-heir of Margery daughter and co-heir of Warwick de Lisle.”). Banks, Baronies in Fee 1 (1844): 254–255 (sub Hoese), 307–308 (sub Marmyun of Witringham), 406–407 (sub St. Quintin) (St. Quintin ped.) (author identifies Margery, wife of Herbert de Saint Quintin, as “sister of Gerard de Lisle.”). Burke, Gen. Hist. of the Dormant, Abeyant, Forfeited & Extinct Peerages (1866): 469–470 (sub St. Quintin) (author identifies Margery, wife of Herbert de St. Quintin, as “sister of Gerard de Lisle, and dau. and co-heir of Warine de Lisle.”). C.C.R. 1346–1349 (1905): 227. C.C.R. 1349–1354 (1906): 283–284. C.C.R. 1360–1364 (1909): 194. VCH Berkshire 3 (1923): 124–133. C.P. 7 (1929): 12–14 (sub Husee). VCH Wiltshire 14 (1991): 215–216. VCH Yorkshire E.R. 7 (2002): 245–254, 306–321. Berkeley Castle Muniments, BCM/B/4/4/1 (available at
http://discovery.nationalarchives.gov.uk). National Archives, SC 8/115/5745 (available at
http://discovery.nationalarchives.gov.uk).
6. Lora de Saint Quintin, married (1st) Robert de Grey, Knt.
7. Elizabeth Grey, married Henry Fitz Hugh, K.G., 3rd Lord Fitz Hugh.
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Source: Online Discovery catalogue
Reference: BCM/B/4/4/1
Description:
Alice widow of Warin de Insula, knight, and Henry Tyeys, knight, her son. Thurs. after St. Hilary, 19 Edw. III
Alice has granted to Henry two parts of her manor of Shyrebourne, and the reversion of the third part held in dower by Margaret widow of Henry Tyeys for her life; to him and his issue, with remainder to Warin de Lile her son and his issue, and her own right heirs.
Witnesses: Aymer de Sancto Amando, Herbert de Seint Quintyn, Robert de Hildesle, knights, Gilbert de Shotesbrok, Robert Hoppegras.
At: Chilton Foliat.
[Please quote GC3126 at Berkeley Castle Muniments when requesting this file]
Date: [19 Jan. 1346]
Held by: Berkeley Castle Muniments, not available at The National Archives