Will 93% lean ground beef stick in a non-stick skillet without oil?
There isn't a way to predict this. Non stick pans are produced in different quality and can be anywhere from "water pearls off the surface" to "as bad as enamel". And all of them lose their non stick properties over time, at wildly different rates depending on quality and usage patterns. 

If you want to know it for your case, you'll have to try it. Worst case, you'll have to thoroughly clean a pan from clingy residue. If it burns onto a white ceramic coating, it can also leave a permanent discoloration, but this is a purely cosmetic problem. 

Update: You can certainly save your meat even if it starts to stick. Use Joe's method from his comment, or simply stir it constantly with a flat edged spatula (I don't know which method is better). If it is patties, loosen them again and again using a spatula, maybe turning them often.