Legally, it would be fine: lobster.rs would get a license, the original poster does own copyright. It's also "clean", if it's done in a manual, selective way. And boom, you get higher quality comments "for free".
Would that be completely unfair to HN?
Imagine that I was one of those cross-posted commenters, and you were not. The comment, as it would show up on lobsters.rs, would start "It doesn't work unless everyone moves over." Uh...what doesn't work? Moves over to where? My comment makes zero sense without the thread context...which is the case with most of my comments. Check out /threads?user=<username> or /newcomments - you can sometimes find interesting discussions that way, but by themselves, the comments are useless.