voltage between L1 and L2 is 240 to a garage door motor, in between this area is the up button that is open, would this voltage change

 

The control for the door opener is via low voltage control. The motor is controlled directly by a up/down relay contacts.
What is your detailed question and concern?
Max.

 

the door dose not rise when the up button is pushed. Meter A reads 240 volts L1 to L2 at all times. Meter B reads 240 volts when the up button is pushed, but no movement of the door occurs. Meter C reads 240 volts when the down button is pushed, and the door attempts to move further down. Based on these measurements, what is the most likely problem?

 

What is the model number of the garage door opener?

Do you hear the motor turn at all ... even if it's stalling?

 

The vast majority of G.D.O in N.A. are made by Chamberlain, There is a generic schematic floating around out there.
When you say L1 L2, what point in the circuit are you measuring?
The up/dwn button and the safety limits etc are usually all low voltage and controlled by a receiver/logic card.
Max.