The microfiber cloth should be sufficient for cleaning any smudges or dirt from the lenses. Using lotion-free soap/dishwashing liquid and water with a microfiber/lint-free towel works as well!
We do NOT recommend using hot water or any chemical-based cleaners on the lenses, and be sure to NOT leave your Felix Grays in the car, on top of a heater, or in an enclosed, unvented space for extended amounts of time (especially during the hot summer months)! Heat and chemical reactions (from alcohol-based cleaning solutions, for example) can affect the AR coating.
Hairspray can also damage the integrity of the lenses' AR coating, so we suggest leaving your FGs off when applying hairspray and waiting for it to fully dry before your lenses come into contact with your hair (or any other hairspray-covered surface).