Yes you need all three.
White is the Neutral, Black is L1 and Red is L2
White to Black = 120 volts, White to Red = 120 volts, Black to Red = 240 volts. The Red and Black are 180 degrees out of phase that is how you get the 240.
The motor and often the timer motor require 120 volts so the unit will not start without the White/Neutral.

Also make sure the wire size you are using is adequate, otherwise you will lower the voltage at the dryer. This will result in poor drying performance and also will cause the motor to either not start and/or overheat.

Just a quicky note to let you know it works.. 3 heavy guage wires clipped in with heavy duty alligator clips.. It's only there as a test line to make sure the motor runs and the heater works.. Now i have it coiled up beside the 240 line where it can't hard a fly unless it's a really BIG fly with 4 inch legs and even then the circuit breaker it turned off. :eek:
Thanks again.