I really like [name_f]Lavinia[/name_f]. I don’t live in the US, so I’m not sure why you would get kickback over it. In [name_m]Britain[/name_m], I think most people would consider it to be a nice name. It’s also fairly popular in [name_f]Italy[/name_f] and Romania.
I would suggest [name_f]Lina[/name_f], [name_f]Liv[/name_f], [name_f]Vina[/name_f], [name_f]Vinia[/name_f], [name_f]Vivi[/name_f], [name_f]Nia[/name_f] or [name_f]Nina[/name_f].
I love it spelled [name_f]Livinia[/name_f]! Then nicknames could be [name_f]Liv[/name_f] or [name_f]Livie[/name_f]. 
[name_f]Ia[/name_f], [name_f]Ina[/name_f], [name_f]Lavin[/name_f], [name_f]Lila[/name_f], [name_f]Lily[/name_f], [name_f]Linny[/name_f], [name_f]Liva[/name_f], [name_f]Niva[/name_f], [name_f]Nivi[/name_f], [name_f]Viva[/name_f]
I do live in the US but it’s not a common name here.
[name_f]Liv[/name_f]
[name_f]Livy[/name_f]
[name_f]Linn[/name_f]/[name_u]Lynn[/name_u]
[name_u]Lanny[/name_u]
[name_f]Lala[/name_f]
[name_f]Nia[/name_f]
[name_f]Ava[/name_f]
[name_u]Avi[/name_u]
[name_f]Lia[/name_f]
Lav
I had a great great aunt named [name_f]Lavinia[/name_f], and she was always called [name_f]Viney[/name_f] (rhyming with tiny)
I have reason to believe [name_f]Liv[/name_f] would work, or [name_f]Viv[/name_f]
LOVE the idea of ‘[name_f]Liv[/name_f]’ as a nn for [name_f]Lavinia[/name_f]!
I think it may be considered too old fashioned or fussy in the US right now (or at least in the small town where I live.)However, I love it! And I wouldn’t let others’ opinions stop me from using it.
[name_u]Love[/name_u] the suggestion of [name_f]Livvy[/name_f]!
[name_f]Liv[/name_f] is my first thought? A little bit of a stretch, but it makes the most sense to me. I think you could also pull [name_f]Vivi[/name_f], [name_f]Via[/name_f], [name_f]Lia[/name_f], [name_f]Nia[/name_f], [name_f]Lana[/name_f], [name_u]Avi[/name_u], and maybe even [name_f]Anya[/name_f]/[name_f]Ania[/name_f]/[name_f]Anja[/name_f] from it? [name_f]Liv[/name_f], [name_f]Vivi[/name_f], and [name_u]Avi[/name_u] would be my favorites, but I also love [name_f]Lia[/name_f] in general.
Good luck!