[name_u]Indiana[/name_u] [name_f]Rose[/name_f]!
[name_f]Lila[/name_f] [name_u]Ruby[/name_u] with [name_u]Indiana[/name_u] [name_u]Rae[/name_u] in second, I also like the suggestions of [name_f]Rose[/name_f] as a middle for either name.
My favorite one is [name_f]Lila[/name_f] [name_u]Ruby[/name_u], though I am unsure of the flow. I don’t like [name_f]Lila[/name_f] [name_f]Rose[/name_f], just because [name_f]Rose[/name_f] is such a basic and predictable middle name. So here are some of my suggestions for [name_f]Lila[/name_f]:
One Syllable:
[name_f]Lila[/name_f] [name_f]Pearl[/name_f]
[name_f]Lila[/name_f] [name_u]June[/name_u]
[name_f]Lila[/name_f] [name_f]Maeve[/name_f]
[name_f]Lila[/name_f] [name_u]Rue[/name_u] (I figured since you like [name_u]Ruby[/name_u])
[name_f]Lila[/name_f] [name_f]Tess[/name_f]
[name_f]Lila[/name_f] [name_u]Wren[/name_u]
Two Syllables:
[name_f]Lila[/name_f] [name_f]Primrose[/name_f] (Since many love [name_f]Rose[/name_f])
[name_f]Lila[/name_f] [name_f]Jasmine[/name_f]
[name_f]Lila[/name_f] [name_f]Colette[/name_f]
[name_f]Lila[/name_f] [name_f]Charlotte[/name_f]
[name_f]Lila[/name_f] [name_f]Autumn[/name_f]
[name_f]Lila[/name_f] [name_f]Delphine[/name_f]
[name_f]Lila[/name_f] [name_f]Meadow[/name_f]
Three Syllables:
[name_f]Lila[/name_f] [name_f]Juliet[/name_f]/te
[name_f]Lila[/name_f] [name_f]Rosemary[/name_f]
[name_f]Lila[/name_f] [name_f]Seraphine[/name_f]
[name_f]Lila[/name_f] [name_f]Mirabel[/name_f]
[name_f]Lila[/name_f] [name_f]Melody[/name_f]
[name_f]Lila[/name_f] [name_f]Marigold[/name_f]
Good luck and I hope I am not too late!
Best Wishes,
Fluffy 
[name_f]Lila[/name_f] [name_u]Ruby[/name_u]. The others aren’t my style but I think [name_f]Lainey[/name_f] [name_f]Rose[/name_f] is really sweet. Good luck!