Plywood will definitely work. I had a very large and heavy tree planted two years ago in the back yard, first using a large tractor/back hoe for the hole and then an even larger fork lift to carry the tree from their semi trailer to the back yard. They were concerned about the weight on my driveway so they laid plywood from the street to the back yard, all on grass. When they removed the plywood there was a slight depression that was gone after a few days and no damage to the grass.
But if your lawn is dry and pretty firm it will probably not hurt to drive on on rare occasions. More often and you will begin to see depressions.