I Speed usage in Lattice Boltzmann Method

One thing that confuses me is the physical speed and sound speed. The lattice sound speed cs=1/sqrt{3} corresponds to the physical sound speed for isothermal flow (sqt{RT}). Why isn't the physical speed (e.g. inlet speed up of lid cavity) converted and use accoringly?

$$c_p=\sqrt{RT}≈330m/s \rightarrow c_s=1/\sqrt{3}≈0.5774$$
Then why isn't the physical speed u map accordingly
e.g. physical speed of inlet(lid) is converted
$$u_p=0.2m/s \rightarrow u_l=0.3*0.5774/330=0.00052491$$

Instead the physical speed u_p is used together with the lattice speed of sound c_s in the flow equilibrium distribution.
$${\displaystyle f_{i}^{\text{eq}}=\omega _{i}\rho \left(1+{\frac {{\vec {e}}_{i}{\vec {u}}}{c_{s}^{2}}}+{\frac {({\vec {e}}_{i}{\vec {u}})^{2}}{2c_{s}^{4}}}-{\frac {{\vec {u}}^{2}}{2c_{s}^{2}}}\right).} $$
 

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