The prion-like spread of protein aggregates is a leading hypothesis for the propagation of neurofibrillary lesions in the brain, including the spread of tau inclusions associated with Alzheimer's disease. The mechanisms of cellular uptake of tau seeds and subsequent nucleated polymerization of cytosolic tau are major questions in the field, and the potential for coupling between the entry and nucleation mechanisms has been little explored. We found that in primary astrocytes, endocytosis of tau seeds leads to their accumulation in lysosomes. This in turn leads to lysosomal swelling, deacidification and recruitment of ESCRT proteins, but not Galectin-3, to the lysosomal membrane. These observations are consistent with nanoscale damage of the lysosomal membrane. Using live cell and STORM, imaging, nucleation of cytosolic tau occurs primarily at the lysosome membrane under these conditions. These data suggest that tau seeds escape from lysosomes via nanoscale damage rather than wholesale rupture, and that nucleation of cytosolic tau commences as soon as tau fibril ends emerge from the lysosomal membrane.