I got one in my 46 gallon. (female though, males get several inches bigger) -- Yes with caution.
Note:
Under Petco lighting they look pinker, under decent LED lighting they will look orange or purple. I don't know why Petco lights distort colors but they do. I thought I was getting a pink female, ended up with a bright orange when I got home. Apparently they only come in orange or purple so that makes sense lol.
They are orange for females, purple for males. Females will turn male in the absence of a male usually. But they do not change back. However in the absence of another female they usually don't complete the change and just start to change to purple a bit and grow the longer fin up top.
Oh also they are not a fan of flake food, they will eat a little of it. But mostly mine eats Mysis. He also will eat brine. But he likes mysis most. He doesn't like krill. I soak my frozen food in a bit of garlic guard before feeding and fish go nuts.
Caution:
I would rate this fish semi-aggressive. I also have a Royal Gamma and the gamma started acting the fool to the much large anthias on day 1, they fought gamma lost. Now he hides from him every times he comes near, and the anthias is aggressive towards him. Eventually long term I may have to re-home the anthias or Royal Gamma, as the gamma used to swim all over the tank and only show aggression if a fish got near his sleeping spot. Now he stays most of the day near his sleeping spot and hides when the anthias gets near. Never travels the tank. He is also eating less as the anthias chases him back in the cave when he spots him out of it too far. Though I do make sure he eats every single day. It is a bit sad, as I like the Royal gamma, and he was fun to watch as he cruised the tank swimming happily before the anthias.
If I could do it over again I would have skipped the Lyretail Anthias. It is a wonderful fish don't get me wrong. But so is the Royal Gamma. However the anthias is not super aggressive to other fish. So perhaps the Royal Gamma just started something and the anthias won't let it go. One way or another I do not think the two will get along. But you may have a different result, if you do I would love to hear about it.