yodaforce
+1y
First off, only "paste" tooth paste will work, plus, it will keep your lights from getting cavities!
Ok, heres how to get the worst case lights clean. Sand with soapy water using 1500-2000 grit sandpaper until the surface is smooth and clean. Then use a rough cutting compound (same compound you would use to do the initial cut on a new paintjob) preferably with a buffer. Then move over to a fine polishing compound, either by hand or with a buffer. The right compounds can clean and polish anything if used properly. I just polished my welding and grinding mask lenses today using the same method and it made them like new again!