A few more (perhaps less intuitive) options:
Aliva (from Old English ‘noble gift’)
Olivera (feminisation of [name_m]Oliver[/name_m], used in the Middle Ages)
Godelieve, Godeleva, Lieve
Madeleva (etymology uncertain. [name_f]Sister[/name_f] Madeleva was an academic and nun in the early 20th Century)
Or (a bit more of a stretch), from first & middle. Something like:
Ylva/Ylvi, Avilla, [name_f]Aviva[/name_f], Avonlea, [name_u]Ever[/name_u]/[name_u]Everly[/name_u], [name_f]Waverley[/name_f], [name_f]Ediva[/name_f], Leneve Everild & [name_u]Averill[/name_u] might also work as middles, especially with a first that has an ‘l’ and ‘i’ or ‘v’ sound (e.g. [name_f]Ludovica[/name_f], [name_f]Lovisa[/name_f], [name_f]Lovina[/name_f])
I think initials [name_f]LIV[/name_f] work (as suggested by @halloween_jacqueline), but also initials LYV or even just LV.