I agree that it's dangerous outside. When I was a child, we lived in the country and my parents let our cat outdoors all the time. She got attacked several times by a stray tom (she was spayed, thank goodness though). This could still happen in a residential neighborhood, as cats are territorial.
I would suggest letting Lola out only when she's supervised, it's much safer. Also, even though it's in a quiet neighborhood with plenty of room, cars are still a threat! Some horrible people will run over whatever is on the road for fun. A friend of mine who grew up on a farm (her dad wouldn't let her have any pets in the house) had several of her beloved cats get hit by cars, and she lived in "the boonies." I'm sure you know all of this already, but maybe you can change your mom's and your grandmother's minds.