Extracellular vesicles (EVs) have received increasing attention over the last two decades. Initially, they were considered as just a garbage disposal tool; however, it has progressively become clear that their protein, nucleic acid (namely miRNA and mRNA), and lipid contents have signaling functions. Besides, it has been established that cells release different types of vesicular structures for which characterization is still in its infancy. Many stress conditions, such as hypoxia, senescence, and oncogene activation have been associated with the release of higher levels of EVs. Further, evidence has shown that autophagic–lysosomal pathway abnormalities also affect EV release. In fact, in neurodegenerative diseases characterized by the accumulation of toxic proteins, although it has not become clear to what extent the intracellular storage of undigested materials itself has beneficial/adverse effects, these proteins have also been shown to be released extracellularly via EVs. Lysosomal storage disorders (LSDs) are characterized by accumulation of undigested substrates within the endosomal–lysosomal system, due either to genetic mutations in lysosomal proteins or to treatment with pharmacological agents. Here, we review studies investigating the role of lysosomal and autophagic dysfunction on the release of EVs, with a focus on studies exploring the release of EVs in LSD models of both genetic and pharmacological origin. A better knowledge of EV-releasing pathways activated in lysosomal stress conditions will provide information on the role of EVs in both alleviating intracellular storage of undigested materials and spreading the pathology to the neighboring tissue.