Not an Irish speaker, but I've seen some of the names and terms while reading folklore. Is it possible that Lug Lám-fada is a proper name/epithet for "Long-armed Lug" (alluding to the god Lug) instead of a descriptor of a "long-armed lug" object?

Yes, she's making a lot of allusions of Irish mythology, and that's definitely a reference to the god Lug Lámhfhada. Also, the word 'lámh' in Irish isn't quite arm. It's your arm below the elbow, including your hand. He has that epithet because for a bunch of reason, not least because of how skilled he is in all things.

The line between folklore and mythology is fuzzy, but this definitely falls on the mythology side of the line.