How to Bake Texture Sequence in Cycles?

I would like to use EEVEE’s Shader to RGB and Cycles’s Fisheye Lnes Camera together.

To emulate Shader to RGB in Cycles, I want to render texture sequence of diffuse passes that respond to the lighting being animated in Cycles.

However, the bake function seems to handle only one frame. Is there a good way to solve this problem?