Is it flat or could take a flat lens? Prying it off and replacing with glass might be the longest lasting option. How old are they?
Polishing plastic, toothpaste will work but being such a low abrasive formula, will take a while. Assuming it is a small lens, might go faster using a cotton swab in a rotary tool to do the polishing, or start with a more abrasive compound and let the toothpaste be the 2nd to last step, last step being an automotive type synthetic polishing sealant, meaning the modern equivalent of paint wax but the polishing type provides that last little bit of refinement.