LGP grants the right to move and jump. Without it a player doesn't have the right to do either when contact occurs. Here is the rule on verticality...
Verticality applies to a legal position. Following are the basic components of the principle of verticality:
ART. 1 . . . Legal guarding position must be obtained initially and movement thereafter must be legal.
ART. 2 . . . From this position, the defender may rise or jump vertically and occupy the space within his/her vertical plane.
ART. 3 . . . The hands and arms of the defender may be raised within his/her vertical plane while on the floor or in the air.
So, until they have LGP, they may have a legal spot by getting there first but when they jump without having LGP, they forfeit the right to their spot....in a sense, they're moving to a new spot above the one they started from and the verticality rule doesn't allow them to do so.