Try BrickStuff. I used to do Lego animation but stopped because it got really expensive.
I would think you would light it like anything else, and try to get some variety and depth into the lighting. Use tracing paper to diffuse the light and reduce the shininess. I believe it is also possible to buy some anti-glare spray if it is a real problem.
Mostly I would think you need small lights, so a couple of LED panels and some little LED desk spotlights would do as a basic set up. Coloured gels help with atmosphere. If you use long exposures, you don't need a lot of light. It's not like live action filming where with 25fps the exposure has to be 1/50th sec. I mostly use 1/2 to 1 second exposures.
One great tip is to use something to break up the evenness of light. In the business they are called cookies, but they are basically either boards with a lot of random shape holes in them or wire mesh with something semi-opaque also randomly placed across it. When these are used in front of the lamp, the faint uneven shadows cast give a nice texture to areas that are otherwise boring to look at. Hope this helps...
I'm also looking at the problem of what lights to use but have come across a wonderful source of diffuser which is an old shower curtain, much cheaper than gels.
Oh, that's a really good tip - but only for reasonably cool LEDs! The reason one had to use special gels on film lights was because they got so hot. With LEDs this is not so much of an issue. I save coloured sweet wrappers at Christmas to use as gels - if only they made bigger sweets!!
The shower curtain idea is great because there are a lot of swirly patterns that might act to break up the light a bit with faint random shadows - like a cello cuccoloris.....ridiculous name for a mesh with swirly patterns on it that can cast uneven shadows onto a surface.
Have a look at this video which talks about them https://m.youtube.com/watch?v=eQSgbHzw3Rk&t=302s
I would think something like this might be what you're looking for?
8"x8" colored cellophane sheets?
$8.99 usd for 104 pieces in 8 colors.