Thanks, Buachaill. there are several "Linne" place names in Scotland, which I suppose would be pronounced "Linn" in English. And there may once have been others.

Steve, you beat me to it. The name in the ballad may well be based on the names in the earlier works.

Or it could be the other way around. The late date of known texts of the ballad, however, makes this an empty assertion.

Probably we will never know. The available evidence - a pair of faery "Tom a Linn" references and a few late"Tam Lane" ballad texts - is just too scanty.

What's undeniable is that people interested in one or both of the songs really, really want them to be closely related.