Well first off, I did not light on this film, so don’t take this as gospel, but here’s a few tips that may help you get something similar.
First off here’s a really useful lighting discussion that has some great ideas, especially if you’re new to lighting…
Lets check your images now, check the first image below for what a rimlight is. Basically, one rule many people follow when lighting is always have a black surface on a white surface on a black surface on a white surface, etc. The idea is to setup your objects into visual layers so that the viewer can easily tell where one object stops and another begins. Rim lighting is one way to help do that. So in the night time image, say you have a darker McQueen against a dark background. Well, the eye won’t be able to immediately tell where McQueen ends and the background begins. So you want to create light and dark planes. In this case, you light the right side of mqueen to be light (probably a fill light, or your key), then the left side of him goes dark, then right at the edge where the darkside of mqueen ends and the dark background begins, place a rim light, which is just a bright light placed such that all you see is a little sliver or edge of light on the corner of an object, so that your image now reads light (right side of mcqueen), dark (left side of mcqueen), light (edge of mcqueen), dark (background). This layering approach is one thing that helps contribute to that slightly cartoony look.
Notice the same pattern in the background of light against dark, see my image number 2.
This also helps define surfaces, say you simplify everything in the scene into cubes. If you’re seeing 2 or 3 sides of a cube, one side should be darker then the other, because then the eye will read the shape of the object. If both sides of the cube are almost the same brightness, then your eye won’t be able to tell what the shape is you’re looking at, and everything will appear flat (which might be what you want in some cases, but not to achieve the look you’re specifically after.) See my image #3 below.
As for the outdoors daytime scene, you can get something similar in any package with a skylight (which will create nice soft shadows), and a keylight that represents the sun. Also notice the use of atmosphere, as things get further they disappear slowly into fog, which gives the scene scale, and notice how the shadow areas go purple, an artistic choice which I think worked beautifully.
And the courtroom scene, all I can advise is a lot of soft lights