22 LR & mower?
First, it might get water soaked and be inert. Assuming it's not inert, the mower would have to pick it up in such a way that the blade would hit the rim, not real likely. Assuming the blade does hit the rim and set it off, it's pretty harmless. It requires the confinement of a chamber and barrel to build up any serious pressure or velocity. Since most people have a rotary mower (as opposed to reel type) these days the deck would confine it unless it happened to be aimed right out the exit port. If you have a bagger that would catch it.
Years ago the NRA ran some experiments in which they used a hot wire to cook off various cartridges under an ordinary corrugated cardboard box. All failed to penetrate the box wall.
The blade would have to catch it just so, it would have to be aimed out the port, no bagger in place, and some one on their stomach close to it to catch it in the eye to do any real harm. A pretty long shot. You're more likely to cause real harm by running over a rock or pipe. We had a case a while back in Australia where a mower kicked out a piece of pipe and killed a pedestrian passing by.