My understanding of the source/history of the name is as follows:
1.) The ethnic roots of the name are MOST UNDENIABLY Irish.
2.) The "motto" attached to the name is "Virtute et Numine," which loosely translates to English as "Strengh and the will of heaven."
3.)The ethnicity is Irish, but the etymology is probably better explained as being English, or possibly Germanic.It comes from "Lawless," and most likely became Lillis as people tried to resolve the English word with Gaelic pronunciation.This also explains why the name is rarely seen in tandem with traditional Irish prefixes (e.g. "O'", et cetera.)
4.)My understanding is that it probably dates back to the GENERAL TIME of the Puritanical Civil Wars in England.(Someone mentioned Cromwell above, so that information jives quite well.)
5.)You can make as many guesses as you'd like as to the way the name was acquired.The most common explanation that I've come across was that there's a history of theft and other wrong-doing somewhere in the family past.
I've never been able to find any information (at least in the leaves along my branch of the family tree) that would suggest this.Try as I might to find something more interesting, all of the ancestors I've been able to peg down were farmers.
The other theory that I've had relayed to me is that the name was given to "the family" by the English themselves, during the multiple centuries of their occupation on the island.The surname could have been granted for innumerable offenses, be it refusal to pay taxes or more mundane things, like disorderliness.I have records of at least one of my great-uncles participating in the events of 1910-1916 that ultimately led to the creation of the Republic of Ireland, and family lore contains more than a few stories on this topic.(Both of my paternal grandparents didn't leave for the United States until the mid-to-late 1920s).
The Germanic etymology of the name itself suggests an English source, but either version of the story is equally plausible.
That's the bulk of what I know.
As for my family, our origins are in County Clare.We're scattered about a bit, but there's a large concentration of my paternal relatives in Ennis, with others in Kilmihil.
My grandfather emigrated to the United States, eventually settling in Buffalo, NY.
HIS father (that is, my great-grandfather) died in some sort of accident when he was still fairly young, and his mother remarried.As a result, I have a collection of half-great-aunts and -uncles who I have yet to track down.
On that note, I'd appreciate any information that anyone might have on that topic.