Yes, place names, as they come down to us, are very important in research. My point about the different spelling of the surname was not meant to be definitive. My research of the area has lead me to the Ordnance Survey Maps. As a licensed land surveyor, that is my natural inclination!
Having examined the Ordnance Survey maps of the Dalry area from the earliest edition to the 1897 edition, the only spelling of the family name on the maps is "Lin" or, more likely, "Linn".
I'm aware of Lynn Street in Dalry, but my point is that all of the Lynns seem to have been long gone before Dalry became a major town. I think that we can agree that the disappearance of the family from Dalry is the unanswered question historically. Of course there are some Linns-Lynns still in Aryshire-Lanarkshire in small numbers compared to the US.
Thanks again for your encouragement, and I will be hoping to provide anything I can to the research.