How fast can a 120VAC LED bulb be switched on and off? (Without serious damage)
It depends. 

There are various designs possible for these bulbs, some of which handle it better than others. It also complicates matters if they're supposed to be "dimmable", which means they try to detect the short on/off cycles applied by a triac dimmer and turn that into a smooth brightness level. I had a set of those that, if dimmed below about 25%, turned into strobe lights.

At least try to use a zero-crossing triac system so you don't turn them on or off while current is flowing. That avoids being detected as dimming.