Putting a wrasse in a tank with significantly larger groupers or lionfish will likely result in the wrasse being eaten. A larger trigger may attack or kill it. A larger puffer is probably a somewhat safer bet, but can still harm it.
If it were my wrasse, I'd take a chance putting it in with a larger puffer or a milder trigger (blueface, crosshatch). You'd likely be ok. But I would never risk it with a much bigger lionfish or grouper or moderate-to-very aggressive species of larger trigger. You'll probably be attending the wrasse's funeral soon after.