I've got a number of animations and I am continually finding and fixing the same problem: my lights change settings over the course of the animation.  When I created the scene I locked all of the lights.  The first time the settings changed, I created a single frame light-set from the first frame to apply to the end frame.  For some reason, it changes the lights on the first frame also, and so I apply it there as well.  When I then scrub the animation it looks fine.  But whenever I load an animation to create a new one from it, the lights will often do it again, seemingly randomly (but always the same changes).  I have a number of clips, and the frequency with which I am seeing this happen goes way beyond what I would expect if it were a simple oversight with just one clip.  It really seems like any of my clips may just suddenly revert back to this behavior, and I can't figure it out.

I had a similar problem when I had too many lights in a scene - turn one on and onother goes off - could it be you have more than 8 lights on ?

Open the keyframe editor and select all but the first frame for all the lights. Then hit del. and delete any keyframes. That will keep all the lights in place for the length of the animation.

Ensure you dont have lights parented to anything.

The usual cause of this behaviour, is unintenionally adjusting lights in some other frame than the first one.
It's easy to do when working on an animation.

If you do that, the lights will be in the same position throughout the animation, but you can adjust them in any frame. Works the same as turning Animating off for a camera.

I am working on a large number of similar animations.  I just noticed that the animations which have the lights moving were all saved on the last frame (it's a project where clips have to match up together, so I am rendering beginning or end frames for comparison).  The clips that were saved on the first frame don't have the moving lights.  I could turn lights animating off, but now I'd have to do it for every clip, and it's quicker to just re-load correct lights.  I should definitely have done that when creating the initial scene though.