I've had the same problem in the past, but not my lawn...which was far worse!
Scaffold boards are handy sized, stiff enough to spread the load, yet allow easy manual handling of the planks.
Usually readily available, and reasonably priced. That said, there's high demand for all this sort of thing at the moment, and good second hand boards are impossible to find hereabouts.
Half inch ply is no good (I tried some old shuttering ply) too thin!