Question
Can I put lye down under my deck to stop vegetation from growing

Answer
Not a good idea. If an animal or a kids should walk through this area their feet could be burned by the lye. A good herbicide would be Roundup. This will kill any green plant. An more organic weed killer is Vinegar. You will need one has a 20% acid (the normal vinegar has about 5 %). The higher % is used in canning. Just spray the weeds with the straight vinegar and they will usually die. Some of the more waxy leaf weeds you may need to add a little liquid dish  soap to the mixture. If you can get under the deck you can put down thicker Plastic and cover with gravel and this will prevent weeds from growing. I hope this helps.