anglers and lions don't mix. lionfish are a favorite food of anglers. and anglers don't mix with any fish that picks at rock, they tend to harass anglers, thinking they have edible skin. the tang and coral beauty could pick at the angler or become its next meal.
the angler needs to be in a tank of its own. I speak from experience. anglers can eat far larger fish than you think, and they are total gluttons. they will eat tankmates eventually, no matter how well you feed them.
if you don't believe me, then read the angler chapter in Reef Fishes volume 1 by Scott Michael. the information is accurate and very useful.