I think he genuinely likes Lady Darkness. Like, this isn't manipulation.
He steals everything, but I bet that song was the first thing someone willingly gifted him, so it meant something for them.
He genuinely loved and appreciated her gift and it genuinely gives him comfort.
Don't get me wrong, he isn't a good person, but he isn't bad.
Remember Iruma literally talked him out of stealing everything else but the thing he actually wanted to steal, even though he lied to Iruma that he had to steal the key to save his brother, even though he could have just lied even more, so he does feel bad.
He knows he is doing bad, but he just enjoys it, but he is also capable of some level of guilt.
So he is just driven by impulse but can be corrected to some degree. So I bet he's gonna get tamed by the girl into not being a scumbag, or at least to not be a womanizer. He will still be a thief, just like she will be always a border partrolwoman, but blossoming with real romance.
Less likely prediction, all the girls he was cheating on were honeypots, and she was the only one he actually cared.