In the long run, yes it is detrimental to his health to just eat one specific food. A major problem with lionfish is lockjaw setting in because of nutritional deficiency caused by exactly your type of problem. Sadly lockjaw is usually almost always fatal. You will definitely need to get him to eat more then mysis in order for him to be a healthy and long lived fish. You can try multiple things from, as the person above said, making the food seem more alive and starving him for a time to see how he responds, trying multiple food types, to soaking the mysis in selcon and/or vitachem to boost the nutritional intake of the food. Also not all live foods are bad. Ghost feeder shrimp seem to be a good, safe, viable choice. You could opt to buy them as you need them, or setup a small breeding tank. A breeding tank would be more beneficial as you can feed the shrimp to increase their nutritional value. He would much rather hunt for the shrimp; however it really doesn't matter how he gets the proper nutritonal intake, all that matters is that he is, in fact, getting it.
Best of Luck with your Lion