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We perform a nonperturbative calculation of the inclusive decay rate for semileptonic decays of the $D_s$ meson from lattice QCD. We present results from a first study based on the computation for the inclusive semileptonic $D_s \rightarrow X_s\ell\nu_\ell$ decay, employing the M\"obius domain-wall action for all quarks. Our reconstruction of the decay rate from lattice data of four-point correlation functions is based on the Chebyshev polynomial approximation approach. We further present a first estimation of systematic effects in the inclusive analysis strategy, addressing the systematic error introduced through the Chebyshev approximation as well as the influence of finite volume effects in our analysis.