buy CLR from your grocery store

Believe it or not coke, the kind you drink will take rust off some things.

If the lounge chairs are metal and its rust, there is a product called Zud, a powder in a can like the cleaner Comet . You sprinkle it on, wet it and let it set. Then get a cloth and rub it and the rust will come up. That might work
you might have to do it more than once

hydrochloric acid