Several systems that create a floating cutting deck for a riding lawn mower are described. The first system is a bar assembly, with a moveable stop, that attaches to and covers the teeth of a lift handle assembly of a conventional riding lawn mower. The second system is a new design for a riding lawn mower that uses a moveable stop (instead of a plurality of teeth) in the lift handle assembly. In both systems, the lift handle is able to move away from the stop (and thereby allow the cutting deck to rise relative to the main frame) when the terrain under the cutting deck is higher than the terrain under the lawn mowers main wheels.