If no, why not?
I find them too close, as they both go consonant, i sound, consonant, “ian” ending, and have the same number of syllables, with stress on the first. If you’ll be using the nickname [name_f]Lily[/name_f] exclusively and [name_f]Lillian[/name_f] is just for the birth certificate, it would be fine, but in which case I would just name her [name_f]Lily[/name_f] and avoid [name_f]Lillian[/name_f] altogether.
If one was a first name and the other was a middle name though, it would be fine.
I saw your other thread too- [name_f]Lillian[/name_f] “[name_f]Lily[/name_f]” and [name_f]Lydia[/name_f] would make a lovely sibset. They’re both classic with a long history of use, but not “core classics” (not like [name_f]Elizabeth[/name_f] or [name_f]Catherine[/name_f]) that were the most popular names for generations.