Depends on the individuals. We have a picasso in with a volitan. They pretty much ignore each other, but the lion has lost fin tips to the trigger (not aggression--the trigger was going after a chunk of scallop and missed). If the lion gets annoyed with the trigger, he'll chase him into a cave, but that seldom happens. More aggressive triggers may snack on the fins intentionally.
The fins will grow back, but it takes a long time. Leo lost the tip about 6 months ago, and while that fin is perfectly shaped now, it's about 1 inch shorter than the rest.