Sounds good. I'm not an expert at Galelic genitives, so I can't say whether íngen Cennétig is correct. We'll have to look it up, if you haven't done so already.
I do know that Lorcáinn is the genitive form of Lorcánn. So, Lorcánn's son would be mac Lorcáinn, not mac Lorcánn. Same with Lachtna and Lachtnae.
We have this problem throughout the Irish tree because people have "corrected" the names.