Most sources agree that the Liles name was originally of French, most likely Breton or Norman, origin. My understanding is that they came to England in the Norman invasion with William in 1062 and as time and history unfolds, became part of the Scottish lowland population along with many others of Celtic origin who became known as Clan Stewart. Most Liles, Lyles and other spelling variations in the, mostly Southern, regions of the US, trace their lineage to ancestors who came to Virginia and the Carolina's with the Scot/Irish immigration of the late 17th and early 18th century .
Nearly all of those surnames in the US trace their lineage back a near common ancestor or small group of Liles ancestors who moved through Virginia down to the Carolinas and then by about 1800 migrate through the South and after the US Civil War many of those families end up in Texas where the migration, for the most part ends.
In my own circumstance, my ancestors are said to have engaged in commerce with England and people of English descent in the Colonies, but the form of how they did their business indicate they had Scottish roots. It is believed that they were a merchant class that moved easily back and forth between English and Scottish societies.
The name Lyle is of Norman French origin, meaning "the island" - L'ile.
The Normans were not really French but were Scandinavian. The French had given them lands in France, "Normandy", basically to stop them being a pest with their continual raiding and in hopes they would settle. In 1066 the Normans invaded and conquered England.
Not only did the Normans invade England, but they penetrated Scotland as well, founding many of the noble families of Scotland. King Robert the Bruce who successfully fought off an English army at Bannockburn established the independent Scottish state was of Norman descent. So were the Stewarts, future kings of Scotland, and the Lyles. They had a castle at Stoneypath, near the village of Garvald in East Lothian, not far from Edinburgh, the royal capital.
The Lyles seem to have fallen from favor in the 1600's and lost their lands and possibly their rank. There are concentrations of Lyles in and around Edinburgh and Midlothian, and also in the Strathclyde area near Glasgow. The Lyles appear to be Lowland Scots rather than Highlanders.
But In Reality
Who knows??? It has been a lot of years so I like to think of our family as "Americans"!