Males and females do lip lock as well. It's supposed to mean they are testing to see if the other is a strong healthy fish suitable as breeding partner. But I have no idea which species do this, and which don't.
But it's mainly males deciding which one is "top fish"
A lot of cichlids lip lock, even discus and angelfish do it. Basically they go mouth to mouth and push each other around. If both partners are similar in strength they might become a pair. If one fish is noticeably weaker than the other, they don't normally become a pair.
When 2 male fish lip lock, it is part of the territorial display. They start out by flaring fins and circling each other. This is a bit like a couple of guys circling and eyeing each other off before they get into a punch up. If the fish are similar in size and neither wants to back down after showing off their fins, they get into it and grab each other by the mouth and push each other around. This will continue until one fish submits and swims away.
They were not the same. One was a peacock. One a yellow lab something. They are fine now. Happened a couple times but now they can get close to each other and it’s cool. I have a 75 gal. Mostly peacocks. 2 yellow labs. And then 4 rainbows. One peacock seems to run the tank. I guess that’s to be expected. He’s the biggest and brightest of them all.