Deborah, there are a couple things I know of that might work. They don't "fix" the scratching, but fill & seal it. One is called "Gel Gloss" and it's for acrylic & fiberglass, as well as some metals, so I think it would probably work on Lucite. I use it on a number of things, and it works great, as it doesn't scratch.
The other thing is an eyeglass cleaner & scratch filler, though I can't recall what it's called. I think it's for both glass & plastic lenses, and puts a clear sort of finish on that fills the scratches. I'd think you could find this at something like a Pearle Vision or some such optical store.
Both of these aren't permanent applications--they need to be done again when they start to wear. But on something like a purse trim or a piece of jewelry, I'd think an initial treatment would last quite some time for lack of heavy use or handling. I use the Gel Gloss on my porcelain bathtub, and an application lasts a long while under heavy use!
