While it's fine to lip some species of fish like bass, it is best to keep your fingers out of a trout's mouth because it puts unnecessary stress on the fish, and because they have small teeth. Keep those hands on the body of the fish!

Can you hold trout by mouth?

In addition, handle the fish with care, and do not grab the fish by the mouth or gills. Instead, cup your hands under the main body of the fish, and control the tail of the fish (at the base) if the fish is larger. NEVER squeeze the fish, as this may damage internal organs or fins.

Is it bad to hold a fish by the mouth?

Fish do revive more quickly when you hold them horizontally for photos and dehooking (Skaggs et al., 2017), though. So, while lipping fish my not harm them in the long-run if you revive them properly (see blog post on fish CPR), it is best for them if you support their belly with a hand as well.