Meaning and origin of Lillis

I am trying to find out excactly where my last name comes from. I'm very sure it's Irish but I think it's pretty un common.

It's a Scottish name but that doesn't mean there aren't a few wandering around Ireland.

[ifhf.brsgenealogy.com]

Said to be Scottish. Its very rare. It is Gaelicised in Ireland as Ó Lillis (pronounced as Oh Lilish).

regards,
Proinsias Mag Fhionnghaile
eolas@mcginleyclan.org