Lye does get placed into barrels eventually. GauHellDragon changed the soap-making reaction to make bars instead of globs, which caused the soap to get stockpiled and also used by the hospital (He said he hadn't noticed the bucket/barrel problem when I asked him about it ), but once that was done, he had dwarves who tried to use soap for cleaning throwing pathfinding errors.
(I asked him to post here, but since he hasn't...)
Does lye get stacked inside of barrels, and if you make soap does the barrel get consumed along with the lye? So far with my test, I've gotten the soap maker to make soap from the buckets of lye... but they use any bucket, lye or no, and then the bucket is consumed. Hrm.
Edit: Yeah the barrel is spared, which is strange considering I pretty much copied the reaction for the bucket variant, which wouldn't work at all. I think the system just can't detect bucket inventory properly, maybe because they don't get renamed like barrels do.
They also wouldn't move the lye into the barrel in Stockpile #1 until I made a Lye-only Stockpile #2, and set it to accept one barrel. And then they moved the lye into the barrel in the former stockpile. Strange.
Another Edit: Soap as a bar will attempt to be used, but always fail and give a pathing error. Soap as a glob will never be used at all, even with containers set up inside of a hospital; the doctor just uses regular water to clean the patients. Soap needs a lot of work, I don't think it's fixable by modding. Heck, if soap is currently set as a glop and is on a floor the dwarves will clean it up and destroy it.