It is best to neuter BEFORE the marking starts, but I have heard of instances when marking stopped immediately after neutering even in an older dog. I definitely would have him neutered---it can't hurt and it might help.
Sturgis was notorious for lifting when I first got him he has since stopped and only does it outside. to mark his territory. i was afraid if he had kept it up i would not keep him. But with time patience and scolding he's done very well. consistancy is the key. when i caught him i used a coke can with pennies and tossed it on the floor next to him when he was lifting his leg. I also put aluminum foil around the legs of my chairs in kitchen thats where he lifted it also helped