If you flip forward through the pages on the link to the original image and look at Lancaster (top) and Son of (left hand columns) on most pages--noting the difference in the formation of the initial letters-- I think there's quite a consistency, pointing to a difference, so that it's more likely to be Sisy than Lisy.
Sisy, variously spelt (e.g., Sissy, Cissy) was used as a diminutive for Cecilia, Frances and Priscilla; perhaps one of those names comes up in the family?
Peter
