What software to use for lighting and rendering 3d animation shorts?
There seem to be a few basic misconceptions here.  For cartoons you don't need anything fancy as long as cell-shading is supported, which is typically a camera filter.

Lighting is actually done in your 3d animation software.  The job of a render engine like Mental Ray or V-ray is simply to process the scene you build to generate the final image, but it takes the geometry, light sources, materials, and cameras that you have defined in your animation software.

I'm personally a big fan of Mental Ray in general, but that's just because of the fact it is included with my 3d animation package of choice (SoftImage).  I thought it was included in most editions of Maya as well, but it might not still be.  I don't remember which render engines are included with Maya, but they should be more than sufficient for your purposes.  For cartoon rendering, you really don't need a hyper-accurate ray tracing engine that can do good physical simulation (which is the point of most of the third party render engines).

Lighting and rendering is also a complex and broad topic that can't really be covered in a couple of simple tutorials.  The basics are very similar to building your model, you just choose the types of lights you want and place them throughout the scene and then place one or more cameras to allow you to render viewpoints.  Lights and cameras can also be animated, just like your characters and scene.

Do your lighting in Maya and try rendering it out in Maya.  If you run in to any specific issues while working on trying to get the look you are going for, you can always post a screen shot here with a specific question and we should be able to offer more directed feedback about how to accomplish what you are trying to do.