Lyla is similar to a lot of other names that are currently popular - Lyla, Lyra, Isla, Layla, Lily, Lola, Delilah etc.
It has three different spellings in use - Lyla, Lilah and Lila
Most of them will probably have popular middle names like May, Grace and Rose, or a filler one-syllable middle name like Jane, Anne, Joy, Hope, Rae.
If your surname is a common one, pick an unusual middle name.
I'd go for a name that's not part of a current trend, as I think it will date, but that's me.