Caught a couple of my Anthias making out!

Actually Al says:

Your 4 Lyretail Anthias (3 females & 1 male) commonly display "kissing" - mouth-to-mouth contact or jaw-locking — as a form of establishing dominance or hierarchy, not courtship or spawning.

Reef hobbyists frequently describe this exact behavior in anthias groups as non-harmful sparring to assert social order, especially among females or when a dominant individual "keeps others in line."