The lawnmower owned by Ludo Bagman's brother Otto is the most important objects in all of the Harry Potter series*! And everyone was obviously so immersed in the lawnmower's awesomeness, nobody thought to ask: Why does Otto Bagman even have a lawnmower?
Assuming Otto Bagman is a competent wizard, he had no need for a lawnmower, which is a muggle artifact. He could just wave his wand and cut the grass.
Here's what Mr.Weasley says about it:
"I liked Ludo," said Mr.Weasley mildly. "He was the one who got us such good tickets for the Cup. I did him a bit of a favor: His brother, Otto, got into a spot of trouble--a lawnmower with unnatural powers--I smoothed the whole thing over."
*No, really. Without this lawnmower, Barty Crouch Jr. might never have stolen Harry's wand, escaped, and Harry would not have won the Triwizard Tournament, and Voldemort would never have come back. Otto Bagman was secretly the biggest Death Eater of them all.