Lilly-Rose or Lilly-Lynne ? x?

hey everyone i want to name my second daughter defiently Lilly, but we really want her to have two first names and a middle name. The reason we choose the Lynne combo was because both me and my partners mums are called Lynne and we wanted the baby to be called something special. We like the name Alexis as a middle or Elizabeth ?? Which do you prefer ?? x