If it is brook, I wish you and your fish the best outcome, because it is a very nasty parasite that requires prompt treatment. You should notice the mucous coating appear thick and opaque on the clown. A quarantine tank (all fish) with formalin (37% I believe), an air pump, and discretionary FW dips would be my treatment of choice for brook. You would then have to let the display tank go without fish (fallow) for 8 weeks to let the remaining parasites die from a lack of host.
I can't comment on the possible lionfish sting, as I haven't experienced that before, however, the white stringy feces and lack of appetite could also suggest an internal parasite. If that is the case, prazipro could be administered (okay to use in your display tank) or fed with metronidazole and garlic.
If you don't have an air pump already installed in your quarantine pump, I would add one to aid breathing of the clown, regardless of the cause. A freshwater dip (match the ph & temp of the quarantine) could also help remove parasites and give it some breathing room, however, in my experience, they can be very stressful to an already stressed-out fish
Good Luck!
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