My father's DNA test from FamilyTreeDNA indicates that his paternal Lynch line is, surprisingly, J2 haplogroup.
Additionally, I was just tested as a part of Ancestry's DNA project and it indicated that I am 7% Middle Eastern. (Ancestry's DNA testing gives results for combined maternal and paternal lines).
A FamilyTreeDNA researcher tells me that she has found no other Irish surname/heritage J2 haplogroup members in her studies. I'm not an expert on genetics, but I believe that R1b is the dominant haplogroup in Irish surnames.
So now the question remains: Are there other people with Lynch surnames who are part of the J2 haplogroup?