For anyone else that finds this old thread looking for an easier fix; try using a microgiber towel with a very small amount of olive oil.
Just rub it in, and wipe it clean.
Thos method does not fully restore the plastic.
On my scooter it went from a visibility of 5% to 75%+
More than enough to see everything in daylight.
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Other good suggestions have been offered here. If you do try any of these, try first on an area of the lens that doesn't really matter. Just in case the result is less than satisfactory.
To do a good job, you probably should look into buying an acrylic plastic polishing kit. They usually contain wet or dry sandpaper in grits from 1500 to 4000 and then a couple of buffing compounds for the final polish. You can get them at most paint and body parts supply houses and some autoparts dealers. Look on-line for "acrylic plastic polishing kits"
Plain old toothpaste works as a great polishing agent.
Polish it with some metal polish like "Brasso" or "Duraglit"
You either polish it or you apply a clear coating. Think about spray-laquer, think about buffing it with an electric drill. Also think about replacing it with glass (possibly the most difficult) L