I'm sure this largely has to do with personality (well behaved, cautious) as it does age, but what is an appropriate age for kids to start using a push lawn mower? Or a riding mower?
We had to go by size and strength rather than age. Our oldest is small for her age, so she and her sister started together. I went by "big enough to push the lawn mower and smart enough not to stick their hands underneath." That turned out to be 12 for the oldest and 10 1/2 for the second. Our third started when he was 10, but mainly because he wanted in on bidding for the job...
I rode my grandpas riding mower at nine or ten. The problem was more a question of not being able to actually do the job than safety at that point, meaning my grandpa had to go out and do it again to get the spots I missed.
So, fun, but hardly useful at that age.
I did, usefully but not enjoyably, mow my parents lawn with a manual mower at about the same age too.