Hi Alex,
There is a [R21 menu] Object Manager> Tags> Material Tags> Bake Texture Tag. There are a lot of options. Crucial in such a set up is a good UV mesh, so no part of the texture overlaps. If the object doesn’t have one, an option is given in the Tag.
There are two main ways, Bake Material or Bake Object (Shift + C to get the Commander, then type in Bake Object)
https://help.maxon.net/us/index.html#5739
https://help.maxon.net/us/index.html#TBAKETEXTURE
An alternative would be to just render from a camera view and use this camera for camera projection to project the rendering back on the object with a new Material.
As a side note, when you bake a single light set up, you can bake another when the light settings change. The two resulting images/textures (or even more), can be then placed into a Layer shader, and animated:
http://old.cineversity.com/forum/forum_posts.asp?TID=2720&PN=1&TPN=11
Scroll down, I have illustrated that set up there. Here is a tiny little demo clip:
https://www.amazon.com/clouddrive/share/aOeu08CRvHTE05jmptWxWbqenzIJj2DwYsWZxiQjRga
If you like me to have a look at a scene of yours, please let me know, I will send you an upload link.
Here is a short run-down:
https://www.amazon.com/clouddrive/share/wGJWQXffPRcoldJuDRanvarAsmZBeWrVsAFGs9HpnD6
Use OpenEXR, any Integer based format will clip anything above 1.0 (100%)
All the best