As
@mattzang noted above sea golides or lyretails can be poo heads to one another especially if you have only 3 or 4. There just isn't enough room for the aggression to be spread out properly. What happens is that one will become the more dominate one and during feeding time chase the others away which in turn force them to hide, miss meals, and slowly die off. They are not like chromis that beat the snot out of them but it is more out of starvation over time with lyretails. You really need a mature tank, lots of corals, and 3 feedings a day to have the group make it - and that food needs to be on opposite sides of the tank...
I've owned 4 and this is what I saw. Very healthy fish. Ate pellet, brine, and mysis shrimp. At first they all got along. Within a week one clearly became the dominate one. I have a 210 gallon tank with 150 lbs of rock. Not that mature so not a lot of corals but lots of nooks and crannies for them to have a retreat. At least once a day they would group up calmly and swim around the tank a bit. Later though they all found their respected area behind a rock or coral to break the flow, and wait for food. I'd add in food to either side of the tank and then the you would see them dart out of their area to strike the food. If you have ever hunted trout (fishing or fly fishing) in a river or stream this is similar to them. They hide behind a rock or tree out of the flow waiting for food - it passes by, they dart out, grab, and then go back. Less energy, right?
Anyway my point is that in time the more aggressive one will start pushing the others away and it limits their food intake. So much that they wither away due to lack of food. They need a lot of food. They are very active. They are fast. They are busy. No food, no energy, death. I lost mine in about 2 months. Reading and research through various forums pretty much followed with what I witnessed first hand. If I am to try again, and I may, then I'd probably go with 12 to 15 of them with the mindset they will have more fish to spread the aggression over. Or buy one male with the 12 to 15 females.
Beautiful fish. Just need to have enough of tank, mature coral, areas to sleep to call their own, and a lot of food otherwise it won't end up well. At least that is what I've seen and read.