Hello,Welcome to our site and thanks for your question. My name isXXXXX and I will do whatever I can to try to help you.
Have you obtained the baptism record of Tomas Varela de Lima, born about 1721 in Ponte de Lima, Portugal? That would be the only way to learn who his parents were. Portuguese records are not available online at all. Records from Portugal are actually very well done, but a descendant must write to the town where the person was born to obtain a copy of baptism records, which usually contain not only the names of the parents and the father's occupation, but the names of grandparents as well.
Once the parents are known, it is matter of finding their marriage record, the marriage records of their parents and then the grandparents, etc. Eventually they may or may not lead to back to Ireland. However, none of the records from anywhere in Portugal are online.
I have been personally on the archives in Viana do Castelo. I did not find nothing about him. I have the deceases register, from Brazil, it is registered like born in Ponte de Lima. But there´s no families there with this names-Varela or Martins living there today. Anyway, in the place he was born, at that time(Refoios do Lima) I met two Irish families living there, Barry and Penny. I think the only mean to find out is by DNA data.
Thanks for getting back to me. I'm a little surprised that you were allowed personal access to the diocese archives in Portugal. Usually access to these fragile old records is allowed is limited to church representative or those they delegate the task to.
The only way that DNA testing will work is if you find someone with the same genetic makeup and you both undergo genetic testing. Even then it only says that somewhere in history there was a common ancestor. It doesn't tell you who that ancestor was. At the current time, DNA testing has only very limited usefulness in genealogy research in spite of all the hype you hear about it.
If whoever did your DNA testing has a database site where you can post your individual results so that anyone may see them, that could be useful. You may meet someone by happenstance that way.
Good luck on your journey,