Lysosome Exocytosis

What happens to to lysosomes?  Do they stay around forever or do they eventually break up?  What do they do with stuff they cannot digest?  In looking for answers to these questions, I've come across reports that lysosomes participate in exocytosis to repair the cell membrane when it is broken http://www.pnas.org/content/101/48/16795.full .  If lysosomes routinely exocytose then that could answer some of my questions.  Perhaps they exocytose when they have fully digested their contents and thereby dump any undigestibles and disappear quietly.  This might explain how the aggregate proteins in AD appear as plaques outside the cell as well as within.  I may also explain how aggregate proteins could move to other cells to seed new mis-folding cascades.