There is a "neutral" position between the individual lever positions. I still don't understand exactly whether there is a difference between the "neutral" position and the "lap" position?
Are you talking about the hold position? Hold basically allows you to recharge the bp and mr when standing stationary at a station so you're prepared to go right when you release brakes.
"Hold" releases the train brakes but keeps the brake cylinder pressure on the loco. As rennekton#1349 said, good for a quick start off the mark. German drivers usually do this by releasing the train brake just before the loco comes to a halt and then applying then loco brakes.
Lap position can also be used for stopping at stations, if you reduce the brake pressure by e.g 10 lb in the apply position then move it to lap, it will keep the 10 lb until you release it, it's good for a gentle and controlled stop once you learn how much to apply the brakes cosidering speed and train weight.