It is hard to remove scratches on lenses with multiple coatings as by trying to remove the scratch, you risk damaging more coating of the lenses. I can recommend using silver polish or just a wax to rub it into the lenses, covering the scratch. However, it is not a permanent solution, so you will have to repeat that measure from time to time. Some people might recommend you completely remove the scratched layer on your plastic lenses with nail polish, but all layers form essential protection for your eyes, so I don’t recommend you to do that.
For other types of lenses, try using non-abrasive or baking soda-based toothpaste or mixture: put it on the ball of cotton or super-soft cloth and gently rub into the scratch, spinning it clockwise for several minutes. Then, wash the toothpaste off the lenses with cold water and take a lint-free cloth to dry up the lenses and remove the used mixture or toothpaste.