Go with the name you like better! [name_f]Lilivere[/name_f] is definitely the choice I’d pick for you.
If honouring your grandmother is really important, and you feel [name_f]Lilivere[/name_f] isn’t enough (although I think it is given the Li connection), make [name_f]Ana[/name_f] or An or [name_f]Anne[/name_f] her middle name!