I was reviewing photos from that show, trying to decide what to use for this post when I stopped at this 1939 Sears and Roebuck Handiman RT and the question began to form. Shure there were bound to be earlier examples of compact tractors but 1939 was still early and the design was heading in the right direction. When you look at these pictures you might think you're looking at what's left of one of these garden tractors but there really never was much more. An illustration from a period ad posted at tractordata,com shows a sheet metal hood covering the Briggs and Stratton engine and that's it. I also read that the hood created overheating problems and many owners just removed them. With a belt drive power takeoff on the single cylinder 376 cc Briggs motor it could conceivably have had a mower attached although that might have been asking a bit much of the little engine.
The David Bradley Manufacturing Co. which was purchased by Sears in 1912 only produced the riding version of the Handiman from 1939 to 1940 so this one owned by John Baum from Appleton, Wisconsin must be a fairly rare collectible. After the war Bradley produced the 2 wheel walk behind Handiman version which became the firms most popular product.
So back to the question at hand. Most sources agree that Edwin Budding patented the first lawnmower in 1830, a reel type mower not much different from the push mowers sold today. Before then grass was not considered a problem as it was taken care of by horses, cows and goats. Around 1893 James Sumner of Lancashire England invented a steam powered lawnmower that was wildly unpopular as most people who tried it agreed that it was easier to cut their grass with a sling blade than keep the boiler fired. In the USA a Col. Edwin George designed a gasoline engine powered mower around 1919 but power mowers did not become widespread until after WW 2 and still no definitive mention of riding mowers. Sure, Cyrus McCormick and others patented horse drawn equipment in the early 1830's that provided a seat for the operator but that was for harvesting not lawn mowing. Beyond this point the water becomes murky indeed. Remember, this was a time when every town of any size had a foundry and machine shop and every boy wanted to grow up to be an inventor not a rock star. (Where did we go so horribly wrong?)
Different sources will point you in different directions. Wikipedia for example has this advertisement for a Ransomes motor lawnmower from 1902 and yes that's a seat. If you turn to page 153 of C.H. Wendel's Encyclopedia of American Farm Tractors you'll see a photo of a McCormick Auto Mower with it's boat tiller steering and a Deering self propelled mowing machine both from the 1890's neither of which were big sellers. Were these the first riding lawn mowers? I wouldn't want to bet the farm on it. If you have the answer or just want to add your 2 cents worth please feel free to post a comment.
Sources and Resources:
Encyclopedia of American Farm Tractors by C.H. Wendel