I guess the question would be how you were going to use LightMix in the animation - it's only possible to use it via the CIE, which would mean manually processing each frame, or via the batch script processing with the CIE, in which case you could apply a single lightmix set up to all the frames (but, you could do that before rendering anyway and render to a different format....)
So there's no way to animate the LightMix settings. You can of course do this manually, simply by rebuilding layers in PS, AE or Premiere, but then you can do that from EXR - either render straight to EXR and the LightSelect layers should still be there and you can build them up in the editing application (Linear Add to blend each LightSelect), and then you can adjust either the opacity of each layer, or manipulate its exposure, or multiply a layer by a color, to manipulate their brightness and color in your editing software.
EDIT - or render to CXR and just batch rename them to EXR, then build up the layers as before.
Hard to say though, without knowing what your planned workflow is :)
ANOTHER EDIT - also, depends on whether you are making an animation from a single still, or whether you mean apply LightMix to an animation (e.g. with a moving camera). A single still is easy enough, same process, load up the EXR into your editing app, build the layers using Linear Add, etc.
