Lysosomes are subjected to physiological and patho-physiological insults over the course of their life cycle and are accordingly repaired or recycled. Lysophagy, the selective degradation of lysosomes via autophagy, occurs upon unrepairable lysosomal membrane rupture; galectins bind to glycosylated macromolecules in the lysosome lumen, orchestrating a series of cellular responses to promote autophagic recycling of damaged lysosomes and transcriptional upregulation of lysosomal genes. Damaged lysosomes are ubiquitylated, resulting in the recruitment of ubiquitin-binding autophagy receptors, which promote assembly of an autophagosome around damaged lysosomes for delivery to healthy lysosomes for degradation. Here, we review the current state of our understanding of mechanisms used to mark and eliminate damaged lysosomes, and discuss the complexities of galectin function and ubiquitin-chain linkage types. Finally, we discuss the limitations of available data and challenges with the goal of understanding the mechanistic basis of key steps in lysophagic flux.