What is the best way to get rid of fleas on cats?

Lemon and water won't work, Dawn is a one-time solution, and the cheap over the counter topicals don't work. Flea shampoo won't work either. The best flea products are those your vet sells. Failing a trip to get one of those, Frontline and Advantage actually *do* work. They are both safe and effective - with the money you've wasted on cheap products, you could have purchased something that will actually work.

Frontline Plus

The problem with the flea spot treatments is they rarely if at all, kill flea eggs. In order to do so, you need a special shampoo that saturates the flea eggs and the internal organs of the fleas. In addition, you need something that won't irritate the skin or cause reactions such as scratching. Add to that flea spot treatments take time to work, shampoo works immediately and kills fleas on contact. Plus it kills lice, mites, ticks and their offspring. It also soothes irritations from scratching and works for dogs and cats. It's economical and lasts a very long time. The link below has it. Best wishes.

Give your cat a bath with regular Dawn dish soap. Make sure to get around their head and behind their ears, but be careful not to get it in their ears, eyes or mouth as it could cause irritation or sickness. Let the Dawn dish soap sit on them for as long as they will let you, or usually about 10 minutes does the trick, rinse all the soap completely off then comb them with a flea comb, you should be able to buy at the store. The comb will pick up the fleas. you might have to repeat, but it should work within the first 1-2 times. Comb them regularly.