Currently WikiTree shows an Alicia (LNAB Bickerstaff) Thornton as daughter of Magna Carta Illustrious Man Thomas Basset. I know of no evidence for this relationship, though it can be found in the usual unsourced type of tree on Ancestry and elsewhere. The Peerage of Ireland, Vol. 3 p. 241 names her father as Simon Bickerstaff. Unless anyone sees just cause or impediment, I intend to detach Alicia from Thomas Basset, with my usual research notes in relevant profiles.
Thomas did have a daughter called Alice, Basset-110, but she married first William Malet and then John Bisset or Biset.