Frances,

After more research this afternoon, I have now confirmed that "Yeigh" means shut or closing in Manx Gaelic. Thus, you were probably correct that the name of the place is Closed Pond or Lake that is Closed. I have found a number of Manx Gaelic refrences with "Yeigh" including the following:
"as yeigh eh yn dorrys" translated to
"and shut the door"

Thus, our name appears to have a Manx heritage, but we are not necessarily from the Loughlan-y-yeigh. I am not sure where to go next, but I feel very satisfied to having found some potential piece of our roots.

Regards, John