If you read the books, I'm pretty sure it was in the second volume where Lugh's mother pressured Tarte to go the extra mile with Lugh. Lugh caught on to this and later reprimanded his mother. Here there was a side comment of Lugh's internal monologue where he said, "Why did you assume that it was my first time." Also when he consummates his love with Dia, he says something like "this is the first time I did it with someone I loved, in place of someone from a brothel." Don't quote me.

Lugh basically cheated on his girlfriend this act can be considered cheating.

Husbands in modern times do it today but is still cheating I can understand is hard to keep your lust under control.

It was toward the beginning of Volume 3 if you want to look, and I’m not sure he and Dia were officially a couple before the Battle of Viekone, but… I’m probably just trying to find an excuse for it. He really did cheat on her.

Lugh by going to a brothel looks manly to any male but this type of thing is used by husbands today to cheat on their wives.