Hey Austin,
don't worry about using lugol's, you can go to your local CVS or similar pharmacy and pick up povidone-iodine- Link bellow is reference to the product, but I've found it at several pharmacies and would bet even a good grocery store's pharmacy would have a similar product.
Buy CVS Povidone-Iodine 10% First Aid Antiseptic Solution online at CVS.com
Not sure if it's the exact same as lugol's, but I'm pretty sure it is and i use it identically for dipping (never dosed it to tank, but I don't use lugols for that either because of the iodate issue)
Here's my recommended procedure that I've used on goni's and lots of LPS's before.
Place into a revive dip, mixed as per instructions (more or less, usually more than less if treating for a disease.) While in that dip (for 3-5 minutes max) use a turkey baster or similar to blow off the diseased or damaged tissue. It's better to be aggressive than gentle here-the diseased tissue will keep spreading, where worst case if you lose some healthy tissue by being too aggressive, the coral should regrow it.
After revive dip, move immedietley into the iodine bath (if you don't have revive/coralrx, go straight to hear and do the turkey baster routine while in the iodine bath.) I mix it up to the point where I can barely see through the water, or if treating a disease (such as brown jelly) to the point where I actually CAN'T see through the water. Of course try and ensure the dip water stays warm during the process, and leave the goni to soak for about 5-10 minutes. Again, i'd err on the side of a bit longer than not long enough with something like brown jelly. After removing, you can use a razor blade to finely cut off any flesh that remains suspicious looking but that didn't get removed with the turkey baster. Put straight back into tank, I don't rinse off in between with some clean tank water, I just go straight back into the tank. Try and put somewhere with decent flow to discourage any possible jelly returning.
As to why it happened- IMO 99% of brown jelly is it getting stung or irritated by something. Can be another coral, or even something small like a vermatid snail or a hydroid. The dip is a perfect time to ensure that none of these little critters are anywhere on the coral and potentially bugging it. Also not a bad idea to place it somewhere different in the tank if possible, just to ensure that maybe a random sweeper tentacle isn't the culprit at nighttime that you might otherwise not notice.
Hope that's some help, and best luck with recovering him!
