I used this name for one of my twins (b.2008), except I added a y after the I to prevent people from pronouncing it with a short I sound. I didn't realize at the time that for most fonts capital I and lowercase L are difficult to tell apart. A lot of people say Lyla the first time they meet her, but at least it rhymes. She doesn't mind much. She loves her name and gets tons of compliments on how beautiful it is. When we chose the name, we had never heard it before, but in the last 5 years I've met a few babies and toddlers named Isla, which sounds the same, even if it's from a different root.
I have an Ila born in 2012! I heard it from my husband and father in law, they were referring to 'Aint Ila Gray' (NC proud). We say eye-LA. It's a beautiful name and we have received many 'ooohs' when introducing her.
It is pronounced eye-la. My daughter has spent most of her life correcting the pronunciation of her name. At her grandmother's request, Illa, we spelled it this way to try to avoid the "ill-a" that she was often called. The Inner Hebrides island, Islay, is pronounced the same way.