If I make some 3D models, white or black as base color, can I use engine lights to highlight details? Or effect of light on RGB channels of the textures count as different colors? In general, is lightning allowed?

The question is quite serious. I can say that the essence of this jam is to create a game with high contrast in graphics. If you are interested, then I can recommend to get acquainted with other 3D from past jams. (Legacy of Light; The Ranger; Impostor Syndrome; Boatmen; BWGameJam2021) As you can see, not all games have only two colors, but the style is still guessed.

One possibility to get gradient/shading even with only black and white/on and off pixels is dithering. 

Image from: https://blog.csdn.net/lz0499/article/details/101627042 Equations for it at this link too. 

I'm not familiar with most engines, but in Godot at least it's not too hard to make a shader,  heres a video:

I imagine it would be possible to replace the color limiting stuff in the above vid with the dithering equations to get a dithering filter.