Your title said anthias but inside the body you mentioned Lyretails specifically. The male is a striking fish. I've not kept them but I do have 4 captive bred Pink Square Anthias from Biota. They can get pretty large up to around 8" or so I've read. Mine are pushing close to 6" now. Very healthy, eat everything, no fight clubs, one dominate in a constant transition state (not full color with square yet), clear harem hierarchy.
I feed a lot. Hourly starting at 0830 ending at 1800. Dry pellet via auto feeder. Small portions mixed blend of mysis, hikari s, a, and tdo x-small, small. I have a variety of fish with some smaller damsels and gobies. Feeding hourly means everyone gets something. I also feed frozen once a day rotating through various foods. PE calanus, mysis, brine, prime reef, LRS reef, LRS fish, LRS Nano.
I've found that by feeding more throughout the day, smaller portions, means everyone is likely to get something. Even the smallest fish in the harem. This works for me and my anthias are all full bodies.