Your description sounds like the geometrical interpretation for time dilation in special relativity except that light beam in the stationary elevator has to bounce off a mirror back to the light source. The observer in the stationary elevator will see the light beam as a straight line.
The observer in the passing elevator will see the light beam travel on an oblique pathway between the light source and mirror. How oblique the pathway, is proportional to the speed of the elevator.
If the laws of physics are broken and the elevator was able to travel at the speed of light(???), the observer in the moving elevator will see the direction of the light beam as being in the same direction as the movement of the elevator. This of course would be perpendicular to the direction as seen by the stationary observer.
Regards
Steven
http://users.westconnect.com.au/~sjastro/small