It's not possible to animate LightMix in C4D or Max. Animating in the CIE would take some very involved scripting, to be honest.
The way people animate LightMix is to set up the LightSelects, leave it at a good default, render, and then recombine the LightSelect layers in a video editor. They can then use Exposure, Color Tint, enabling/disabling layers, etc. in the video editor, animating those there.
(Should add that this requires 32 bit output, and the Linear Add would be the process for stacking the layers)