Reo did make some odd looking mowers. I remember something similar to that as a kid, a buddy's dad had one in the shed that was too far gone to mow with.
It was Gulf blue and white. It had an odd brand engine, I'm not sure what it was, I think the reason it sat was due to lack of motor parts or something.
Another older neighbor used a Reo rear engine rider, also painted the same color blue, which had an old Lawson motor mounted in the rear.