Last winter I read about cleaning ski goggles which sometimes require extra care to avoid removing the anti-fog coating. Folks recommend breathing on the glasses & wiping them with the soft cloth goggle bag. OTOH Smith says their goggles' coating doesn't get dissolved with mild dishwash (Dawn) detergent.
For bike glasses, how about using Dawn + fingertip or microfiber cloth to wash & perhaps microfiber cloth to dry if necessary? Microfiber cloth is very popular among car-detailing fans for being gentle on delicate finishes; caveat being that it's clean & free from any grit.