The linear Boltzmann equation provides a physically accurate model for charged particle transport. This is essential for applications such as radiation therapy, where dose deposition must be carefully controlled. However, solving it numerically is challenging due to multiscale effects, a high-dimensional phase space and strongly forward-peaked scattering. The resulting need for finely resolved phase space discretizations or specialized methodological modifications often leads to prohibitive memory requirements and computational costs. The dynamical low-rank approximation (Koch and Lubich, 2007) has been shown to be very effective in reducing dimensionality and thus computational costs in a variety of kinetic problems, including electron and proton transport (Kusch and Stammer, 2023; Stammer et al, 2025). In (Stammer et al, 2025), we combine the rank-adaptive DLRA integrator from (Ceruti et al, 2022) with a second order finite volume scheme and a very high order moment method (Pn) for proton dose calculations. While cost reduction down to 0.05% of runtime and 0.004% of allocated memory are achieved compared to a full-rank computation, the spatial and angular resolutions required to compete with gold standard reference codes exceed what is customary in application and small negative regions remain. To tackle these issues, we now explore a combination of dynamical low-rank approximation with locally refined spatial discretizations. For this, we refine the spatial domain using octrees according to the expected dose distribution, computed using a cheap heuristic approach, as well as tissue density. First results indicate that the possibility of strong refinement in regions with steep gradients, such as near the Bragg peak of a proton beam, is very effective in eliminating negative regions and allows for a significantly smaller number of spatial cells over all. We further discuss the implications of non-uniform refinement on the energy step restriction and strategies for efficient GPU implementation.