The distribution of absorbed dose in radionuclide therapy with Lu$^{177}$ can be approximated by convolving an image of the time-integrated activity distribution with a dose voxel kernel representing different tissue types. This fast but inaccurate approximation is unsuitable for personalised dosimetry because it neglects tissue heterogeneity. Such heterogeneity can be incorporated by combining imaging modalities such as computed tomography and single-photon emission computed tomography with computationally expensive Monte Carlo simulation. The aim of this study is to estimate, for the first time, dose voxel kernels from density kernels derived from computed-tomography data by means of deep learning using convolutional neural networks. On a test set of real patient data, the proposed architecture achieved an intersection-over-union score of $0.86$ after $308$ epochs and a corresponding mean squared error of $1.24\times 10^{-4}$. This generalisation performance shows that the trained convolutional network is indeed capable of learning the map from density kernels to dose voxel kernels. Future work will evaluate dose voxel kernels estimated by neural networks against Monte Carlo simulations of whole-body computed tomography in order to predict patient-specific voxel dose maps.