I am installing LVP now with attached pad, additional pad will void your warranty. Anyway, you don't want too much cushion as this will affect the locking of the planks.
You can also verify through manufacturer/installation instruction as I did.
The proper way is to replace the piece, but this is either laborious if you have to replace planks until you get to the damaged one, or it is very difficult and risks damaging the rest of the flooring, especially if you attempt lifting it out by lifting and wiggling the whole floor.
This assumes it's a click-in type.
If you have an extra piece for ...
American manufacturers don’t use asbestos in vinyl products today, but other countries continue to use asbestos in vinyl products and there’s no regulation on importing them into the U.S. I'll highly suspect the product from China.
The following brands of vinyl flooring contained asbestos: