The process of a lysosome attaching to and breaking down something else is called "Heterophagy", meaning "other eating".
Material to be digested is "endocytosed", brought into the cell via phagosome ( phagocytosis ), pinocytotic vesicles ( pinocytoses ) or coated vesicle ( receptor mediated endocytosis ).
The coated vesicle merges with the lysosome, forming a secondary lysosome.
The contents of the secondary lysosome are acidified and the lysosome membrane pumps hydrogen ions into the coated vesicle or phagosome and its contents are digested.
Useful materials are ( released into cytoplasm?, transported to other parts of the cel? ) and waste material is encased in unit membrane and excreted or stored...?