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ABSTRACT: Most conventional approaches to calculate perturbations of a Kerr black hole involve solving the Teukolsky equation because it is separable into spheroidal harmonics. Despite the many advantages of the Teukolsky equation, usage of Teukolsky solutions to describe orbital evolution (like with radiation reaction forces influencing extreme mass-ratio inspirals) leads to considerable difficulties; examples of associated difficulties include pathological gauge features after metric reconstruction and obstacles impeding calculation of higher order perturbations. This work aims to avoid many of those difficulties by calculating the metric perturbations from a small body orbiting a Kerr black hole directly in Lorenz gauge without separating into spheroidal harmonic modes. This approach leads to a system of coupled elliptic PDEs that we solve numerically to determine the metric perturbation and radiation reaction force. By successfully calculating these perturbations through second order in the mass-ratio, we would be able to describe the orbital evolution precisely enough to enable high precision tests of general relativity during LISA data analysis.