An ex-coworker of mine got a pair of goggles that he could put over his prescription glasses. In his case not so much because of dirt on the lenses, but because wind bothered his eyes.
A lot of the ones you'll find are the high-durability ones for mountain bikers (with thick heavy frames), but it is possible to find lightweight (and not so ugly ones) like ...
There are cycling helmets with integrated detachable visor. The visor covers the eyes. Yet the helmet is open below.
I see them frequently on my commutes on rainy days. Most are urban style helmets. Ventilation might be a little lacking for very high temps and high exertion.
Here are two arbitrarily chosen examples:
I can't think of a way to keep your glasses from getting dirty. It sounds like the dirt could be carried by the air. As you ride the air hits your glasses and gets them messy.
If you get laser surgery so you don't need glasses then all the stuff you clean off your glasses will go straight into your eyes.
You need something to protect your eyes and is easy ...