Different "levels" of velocity?

I’m having a bit of trouble sorting out what velocities are actually what in LBE. The way I sort of understand it right now, we really have two levels, so to speak, of velocities, in the model. In applying the model, we have the lattice velocity which determines where a specific distribution function move in the streaming step. Underlying that, each distribution function carry information about actual particle velocity, by telling us how a large amount of velocities are spread out across an interval. But exactly how do you make the link, how does the physical velocities decide what the lattice velocity should be? I do understand that this is quite likely a very naive question, but as I mentioned earlier, I don’t have anyone to discuss this with around here, so I tend to get hung up on thoughts like this and can’t really get anyhwhere, because I keep wondering how wildly I veered of the track. Any input greatly appreciated!