What if a lecturer has to use the bathroom while on stage? If a student has to use the bathroom, s/he may simply politely and quietly excuse him/herself for a few minutes.

But is there any established etiquette for what an instructor is to do when nature suddenly calls?  Let's say this is a typical classroom lecture of about 90 minutes, meaning a student body of about 80-90 and no scheduled breaks.

Oh, also, let's assume that there's no real illness or other crippling circumstance that forces the instructor to leave; just a good old-fashioned porcelain inspection, resulting from consuming just a bit much V8 an hour earlier (seriously, that strawberry-banana V-Fusion is addictive).
Ideally, you use the bathroom before lecturing which should prevent you from needing the bathroom during the lecuture. In cases where you are unwell, I find it best to let the class know ahead of time to tell them you are unwell and might need to suddenly excuse yourself, but that you will be back.

Regardless of if you have told the students in advance, if you must excuse yourself, do it politely and tell them you will be back in a few moments.