If you want a pedantic explanation, here’s all my linguistic training spilling out : D.
[name]Lila/name makes sense. Look at [name]Delilah[/name]. English spelling is weird. If the fact that [name]Lily[/name] has the sound you want on the i is weird to you, read further and I have a sentence on that below. But [name]Lily[/name] is the oddball here, not [name]Lila[/name], and this is probably why the spelling [name]Lilly[/name] (and for that matter [name]Lillie[/name]) exists as a back-up.
I feel your pain somewhat. I am annoyed that the prn [name]Myla[/name] can’t be gotten from [name]Mila[/name] (Mee-la), because [name]Mila[/name] Kunis uses an Eastern European prn and has popularized the name that way. But such is life, and [name]Lila[/name] isn’t [name]Lilla[/name] for different reasons than this.
i by itself can in fact say the long sound “eye” IF it is the last sound in a syllable. In the spelling [name]Lila[/name], there is nothing in the spelling to tell us to stop, and so we break between the i and the l, leaving i by itself, with the long sound (the spelling doesn’t determine the syllables, but rather the other way around, but the spelling often gives us a clue).
We see this all the time in words like bicycle (bi cyc le, likewise the y makes a short sound because the c closes the syllable), binary, dinosaur, dioxide, really just anything with the prefixes bi and di. In words like limousine or little, the i is short because the syllable includes the following consonant (lim ou sine, litt le).
For the same reasons, [name]Leela[/name] and [name]Layla[/name] for [name]Lila/name doesn’t really make sense, and I’ve actually never seen those suggested! I have seen occasional posts that people like [name]Lilah[/name] or [name]Lyla[/name] or [name]Lylah[/name] over [name]Lila[/name] because it seems to make the long i sound stricter. I don’t really agree, because [name]Lila[/name] is in fact following English spelling rules, but it is probably a borrow from [name]Delilah[/name] and [name]Myla[/name], where it does in fact seem to have that effect.
In our spelling system, l is a frequent doubler when it is at the end of a syllable with a short vowel (f and s are the two other letters like this). Look at all, taller, silly, etc (and for f and s, off, cuff, riff, mess, lesser, crass, etc.).
There are exceptions of course, but this is the general rule. [name]Lily[/name] is an exception to the spelling rule, but it’s not breaking the syllable rule ([name]Lil[/name] y). If it weren’t for habit of saying [name]Lily[/name] as a language the way we say it, Lie-lee would be a completely reasonable guess at the prn. [name]Lilly[/name] or [name]Lillie[/name] is following the spelling rule.
This is why the pp is right, for the prn you like, [name]Lilla[/name] makes sense.
What else…gila monster, like the lizard, is another exception (hee-la), but that’s because it’s borrowed from Spanish (we also don’t pronounce g like h regularly : D ).
Good luck!
/virtual hug.
lol