How the direction of radial vector in lattice space related to direction of momentum in real space?

In Photoelectric Effect, the density of states not only depend on the magnitude of the momentum but also on the direction of the momentum, we have to incorporate this in calculation. This is done by using box normalisation convention and claiming that the direction of the radial vector in lattice space($n_{x}$, $n_{y}$, $n_{z}$ as axes) is same as the direction of the momentum. I couldn’t understand this part, how is the direction in lattice space have relation with directions in real space?