Do you know what you are treating the fish for? Are the spots you are seeing salt sized dots or are they more powdery and dusty in appearance? I'm assuming the problem is ick.
Better to treat all the fish with hyposalinity if you have a clear diagnosis of ick. Coppersafe is not all that safe, and it requires diligence in terms of maintaining therapeutic levels. Hyposalinity is the better choice for treating ick. However, if you are dealing with oodinium [velvet] then you will have to treat with copper.
While Franks comments are very correct relating to the lionfish, its shedding and its lower tolerance of copper, I’d add that as long as the lion is in the main tank, he is a host and propagator of the parasite. Even if the lion resists infestation, he will host the parasite in your tank; thus, when your other “well” fish return to the tank, they will be exposed to the parasite again. It is advisable to treat all your fish, preferable with hyposalinity in the case of ick, rather than with coppersafe.