the way it looks in the video games
I have never played a lego game but I suspect that they use texture swapping. Here is one old tutorial. I’m sure that you can find better ones.
I think that’s going to be a 2d animated face mapped as a texture onto a 3d head. I prefer the look they used in The Lego Movie, which can be achieved with texture swapping and a whole lot of slight variations on the basic mouth shapes. Facial animation, especially lip syncing, generally looks better with more holds than tweens.
I made this using something like 10 different mouth shapes. It’s a little choppy but if you add another 10 or 20 to transition from one phoneme to another it would look pretty smooth.
I’d really like to see you posting some actual images here instead of expecting us to see or to have seen the movie or played the video game.
I suspect that you could do a lot of this fairly easily with shape-keys: the mouth region would consist of a grid of boxes and each shape would be an extrusion/recess of selected boxes. Transitions between those keys would then be very abrupt … possibly just one or two “in-between” frames so that the image does not “literally flicker.” The facial (and cheek-like) features would only move in-and-out as though the animation were being done by adding and removing Lego parts, as, in a stop-motion film, it could be.