This is not scientific by any means, but whenever I see an "-ah" at the end of a name, I think of Biblical names like
Delilah,
Hadassah,
Tovah,
Deborah,
Hannah,
Leah,
Sarah,
Susannah,
Micah,
Jeremiah,
Elijah, etc.
Lila fits into a different category in my mind, old fashioned names popular in Victorian / Edwardian times.
Of course there are exception to this, it's just a general preference in my own mind. When I see Lilah, I ask myself, "where's the 'De-' part?"