I'd use a non-petroleum distillate lubrication on tires because prolonged expossure will cause failure. Granted, a tire could soak in a mineral oil or diesel fuel overnight and only be softened up, but for mounting the tires to the rim I would use a water-based lube (like wire pulling lube or something) to get them on there. That way no oil would be left inside the tire, leading to eventual failure. I would soak the tires in something to soften them only after they're mounted to the wheels.