Have a lamp rotate around a fixed spot I want to have 3 lamps in a group that are supposed to rotate around in a circle. However, I want the light rays to remain shining onto a fixed spot as it rotates. 

Do I constrain it to an empty or what is the best way to go about this? Will it still work if the lights follow a path?

Thanks for your help.
Make the light follow the path with a Follow Path constraint, Target should be the curve that you want to use as path.

Then add a Track to constraint. Set the Target to the empty (or object you want the light to point to)  with the following settings:

To = -Z

Up = Y