2N7000 NMOS only switches properly when gate and source is connected with 1MΩ
With your multimeter or the resistor, you are providing a path to ground at the gate. The gate is essentially a small capacitor, and is very high impedance. This means that charge may accumulate, and raise \$V_\mathrm{gs}\$ sufficiently to allow the MOSFET to conduct. Hence, your LED was lighting up. It is always good practice to include this "pull down" resistor.