in a non-relativistic approx. the Lorentz force does not depend on the choice of the intertial reference frame
F=qE+q(v x B) the formula is vectorially written
in the frame of the elevator the u r having some vel and the electron is also having some vel so acc to Lorentz expresiion the value of v has changed but the correcponding value of E has also changed in ur frame keeping the net force constant.
actually there is division of the force into electrical and magnetic comp.
so i think that there is the transformation of magnetic force into electrostatic force !!!!
tell me if i m correct?