Although lime will work just as well as lye, you simply cannot substitute lime for lye because lye is very water soluble and lime is barely soluble at all.
5 tbsp of bark is probably only 75-100g bark, SWIM would recommend scrapping it if you have more bark, it will take a lot of time and work to fix the extraction which may or may not work.
Maybe try doing a proper lime-tek while you are waiting. (SWIM hears q21q21's tek work well... haha)
While doing a fresh tek take the mush and leave it sitting out in a baking tray or something for a week or so until it no longer smells of naptha (DON'T put naptha in the OVEN!) then you can put the tray in the oven at LOW until it becomes like mud. Then begin your work.
You can post any question you have about the tek, though please look through the tek and don't ask questions that are clearly stated in the tek.
Cheers