Bully types that lie quietly and watch are every bit, if not more, potentially dangerous as the barkers and those that show teeth and growl so it's good you know his history if you think a quiet bully type might not be threat.
Most shelters these days won't sell pittie types to anyone and kill them if the owner doesn't claim them, as they are so often abused by fighting or baiting with them and cost them so much of their monetary resources to house. They are by far the most-surrendered or abandoned breed type these days. And why chance even trying it with a shelter when he can be taken from that yard with a meat lure or a catch-pole and go straight to the fight compound, free and clear?
I'd take heart. For some reason, in my experience - and I know that's extremely limited - in all but the most pit-devotee homes there are that I've known - the casual owner of a pittie with a troubled past of attacks doesn't ever seem to keep him for his full lifetime. Something always seems to happen and suddenly, the dog is gone.
Maybe you could try carrying Lola from the car to the house in a hardshell airline carrier as you whoosh open the umbrella with the other hand and walk into the house if the dog is out in that yard when you get home.
I'll sure be praying that you and Lola don't fall victim to this dog.