Frederick L. Weis in "Ancestral Roots---," 6th ed., line 117, gives Alice de Lusignan, dau/Hugh XI de Lusignan, Count of Ponthieu, La Marche, and Angouleme, by his wife, Yolande de Dreux, as her parents. No dates, except marriage [1253] are listed for her, but her father was b.1221 and d.1250 (in Egypt) and Gilbert de Clare is listed as b.1243 and d.7 Dec 1299---so, c.1245 is close for her year of b.
Cokayne's "Complete Peerage" (Berkeley, p.129)