After your sets are constructed, but before you start shooting your scene, you'll want to set up lighting. Proper lighting will let the viewer see more clearly what's going on in each scene, help you simulate different types of settings (such as daytime, nighttime, indoor, outdoor, sunny or cloudy) and prevent shot-to-shot light changes that can cause unwanted flickering effects in your final film.
Ideally, you want to either film in a room with no windows or somehow block the windows to keep natural light or other external light from coming into the room. You can use blackout shades, blankets or anything that will fully block out any outside light. You will probably also want to keep doors to other rooms shut to keep out other household light. It might help to inform roommates or family members that you're shooting so that they don't walk in on you. Also be sure to wear dark clothing, preferably black, since light will reflect off of white or light clothing onto your set.
You'll probably want to light your sets and characters with multiple lights to get the brightness and shadow just right. You generally want two or three lamps you can position on or near your set, at least one for front (or key) lighting and one for backlighting. To add fill lighting to reduce shadows, you can use another light, or something white, like a piece of paper, to bounce light onto the scene where needed. You might also want to place a diffuser (again, maybe a handy sheet of paper) over the lamp bulbs to soften and spread out the light and prevent harsh shadows.
You can alter the lighting by changing your brightness and contrast settings of the camera or software. You should feel free to play around and take test footage to see what works for your goals. There are plenty of online tutorials for lighting stop-motion, or specifically brickfilm shoots, to help you get started and avoid pitfalls.
Still, film is an art form and there are few hard and fast rules. Filming in natural (i.e., outdoor) light is usually considered a stop-motion no-no since it changes constantly (causing the dreaded flicker), but people have successfully incorporated outdoor shots into their brickfilms.