So you have a lever with 4 to 6 foreward gears then Neutral and finally reverse with a sort of dog leg to go from foreward to reverse.
This means you have a manual gearbox with real gears.
Run through the entire box make sure all the gears work.
This box actually has a neutral where no gears are selected.
AFAIK there is no adjustment on the gear change lever so you have either bent the selector or the detent in the box is worn.
If you follow the gear change rod to where it goes to the tranny it should slot into a lever.
Disconnect the rod from the lever and move the lever by hand ) you will need a shifter on it as it should be quite stiff.
Check that it "clicks " into place for all of the gears, count them, from top all the way back through neutral to reverse.
If they are all quite firm then select neutral and try pushing the mower along the ground.
It should move easily and freely.
In that case the gearchange rod will need a little bending so that when in the neutral gate, the box is really in neutral