First my questions on cleaning up! I've been using warm water with dish soap, is that decent? Mom suggested that hotter water would work better, but I can't stand hot water

I use tap water around 100-110 *F
My second question is to do with surface protection! Is freezer paper a good idea to keep the table protected? When I made my HP I didn't use anything, and I spilled a drop of lye water, its still slowly eating the table and we've been unable to stop it as its inside the wood fibers now... oops! Since then I was using waxed paper, which I discovered isn't soap batter-proof. Tonight I tried freezer paper, seemed to work well, but I figured you folks would know better than anyone =D
Here is a picture of the table, so folks can see what lye can do. This is a lacquered solid pine table (now with fancy chemical burn hole!) I dug out most of the remnants of wood that the lye has dissolved, its about 1.5 mm deep. It doesn't burn you if you touch it and I couldn't get anyone to zap test it =P I THINK I've got it neutralized now after a nice soaking of vinegar. I'll know for sure in a couple days.

Brief edit: only the round hole is from lye water, the rest of the damage is from other crafts, and moving big heavy snake vivariums which made the deep scratch like marks. Again... oops? Well used and loved table!