Dear Vaibhav,
With LBM, we usually store one or several distribution functions f at each node. From that we compute physical quanteties like the density, pressure, velocity, temerature, stress, … as moments of f. There is theoretical evidence that you get macroskopic equations like Navier-Stokes, convection-diffision, even Maxwell up to a discretization error! Have a look in the standard literature or (and ;-)) come to our next spring school which takes place in Karlsruhe.
Best
Mathias