If you mean like where the circle turns into a bowl:
Then the answer is yes, you can either do it by creating the in-between frames by hand or by shading a 3D object you create in C4D Lite so that it looks like it is 2D by using a cartoon shader. Both require both skill as an animator and a bit of study to pull off. There is no effect that will give you this automatically. The shot where the guy does a flip:
could also be done both ways, but it would require drawing skill if you did it by creating the animation by hand. A cartoon shader on a 3D object object using C4D would also require a lot more skill. Personally I would probably go with the 3D animation with a cartoon or cell shader because my 3D skills are faster than my hand drawn cell animation skill. Here's a tutorial on how to do cell shading in Blender, an open source 3D app that I use a lot: cell shader in blender internal on Vimeo
Thanks for getting back to me.
Just to check: will the tutorial you've posted there from Blender be transferable to C4D Lite?
The theory of the tutorial is the same, the procedure is different. I'm sure you can find a shading tutorial for C4D that would work but remember that the Lite version is limited in what it can do. I personally have not tried to do cartoon shading in the free version.
To get the "vector look" in Cinema 4d without using a cel shader, create all textures with 100% luminance. This will flat-shade everything as long as the luminance channel is the only thing checked. Because everything is self-illuminated, no lights are needed in the scene.