The paper is devoted to stability analysis of discrete-time time-delay systems, obtained after explicit Euler discretization of (locally) homogeneous continuous-time models. The results are derived by applying the Lyapunov-Krasovskii theory. A generic structure of the functional is given that suits for any homogeneous system of nonzero degree (and it can also be used for any dynamics admitting a homogeneous approximation). The obtained conditions are utilized to demonstrate stability for a discretized delayed locally homogeneous planar system with negative and positive degrees.