Yeah, but it couldn't trash itself, and I think that was the point. As Sudgy implied, Lose Track is only about moving cards. The BoM-Raze couldn't trash itself because it can only trash (move) itself from the expected location, the play area. But it can still be played (so it gives you +1 action and lets you trash a card etc) - a card can be played no matter where it is. You fail to put it into play, because of Lose Track, but you still follow the instructions. It's just, that's the rules.
I'm still unsure.
Throne-Raze can't trash itself a second time, because (a) you can't trash your trash, (b) it thinks it's in play but it isn't (c) both reasons would apply? IIRC, you can still
choose to trash itself, but it fails and you only get the +1 Action.
So Throne BoM-Island BoM-Raze (a)
can trash itself because it's not in the trash, or (b) can't trash itself because it's expecting itself to be in play.
Is it implied in the wording of an Action that it expects itself to be in play, because that's where cards that are played usually are? I'm sort of thinking that (b) is how it works, but... really, you could get a PhD in Lose Track Rule. Maybe.