Two months is not a lot of time, especially since you (presumably?) won't be working full time on it.
Anyways, here are two programming heavy ideas from the top of my head:
Global Illumination is kinda hard, especially given your limited time frame and experience. However, this comes to mind:
It is a neat approach that might be feasible in the two months if you push yourself a bit. There seems to be code if you get stuck and you might be able to come up with some creative improvement.
Another idea I always wanted to implement that involves light, although in an unusual way, would be a content creation tool that helps with texturing models. Usually, triangle meshes are unwrapped and then the textures are painted directly. You could create a tool where instead of directly painting the final texture(s), you set up a couple of projectors around the object, like spot lights which project an image (hence the need for light and shadows). The artists would then paint the images of those projectors and the final model textures would be baked by your tool. To some degree this is already supported in the major modelling packages but you could enhance it by allowing projectors to mix and combine colors so that reusable dirt or rust decals can be added on top. You could also allow the projectors to not only affect the color textures, but also the textures for the other material parameters.
The downside is that such a tool can be rather GUI heavy. The upside is that you can easily "scale" the project according to your progress. Eg start with a purely non-gui application that reads the projector positions and mesh from a blender export, displays a preview, and performs the bake. Then add features like GUI, different projector types, etc until the two months are over.