In an animal cell, what is the function of the lysosomes?

Release enzymes outside of the cell (exocytosis)
which may serve the purpose of destroying materials around the cell.Break-down 'digestion' of materials from inside the cell (autophagy) 
i.e. by fusing with vacuoles from inside the cell. 
This could include digesting worn-out organelles so that useful chemicals locked-up in their structures can be re-used by the cell.Break-down 'digestion' of materials from outside the cell (heterophagy)
i.e. by fusing with vacuoles from outside the cell.
This could include breaking-down material taken-in by phagocytes, which include many types of white blood cells - also known as leucocytes. Specific mechanisms of heterophagy can be:phagocytic - by which cells engulf extracellular debris, bacteria or other particles - only occurs in certain specialized cellspinocytic - by which cells engulf extracellular fluidendocytic - by which cells take-up particles such as molecules that have become attached to the outer-surface of the cell membrane.Recycle the products of biochemical reactions that have taken place following materials being brought into the cell by endocytosis (general term for this 'recycling' function: biosynthesis) 
Different materials (chemicals) are processed in different ways, e.g. some structures may be processed/degraded within lysosomes and others are taken to the surface of the cell.Completely break-down cells that have died (autolysis)

In general, the functions of lysosomes involve breaking-down i.e. processing to 'make safe' or make use of, or removing from the cell e.g. by exocytosis, useless and potentially harmful materials such as old worn-out parts of the cell or potential threats such bacteria. Lysosomes can therefore be thought of as the rubbish disposal units within cel

Release enzymes outside of the cell (exocytosis)
which may serve the purpose of destroying materials around the cell.Break-down 'digestion' of materials from inside the cell (autophagy) 
i.e. by fusing with vacuoles from inside the cell. 
This could include digesting worn-out organelles so that useful chemicals locked-up in their structures can be re-used by the cell.Break-down 'digestion' of materials from outside the cell (heterophagy)
i.e. by fusing with vacuoles from outside the cell.
This could include breaking-down material taken-in by phagocytes, which include many types of white blood cells - also known as leucocytes. Specific mechanisms of heterophagy can be:phagocytic - by which cells engulf extracellular debris, bacteria or other particles - only occurs in certain specialized cellspinocytic - by which cells engulf extracellular fluidendocytic - by which cells take-up particles such as molecules that have become attached to the outer-surface of the cell membrane.Recycle the products of biochemical reactions that have taken place following materials being brought into the cell by endocytosis (general term for this 'recycling' function: biosynthesis) 
Different materials (chemicals) are processed in different ways, e.g. some structures may be processed/degraded within lysosomes and others are taken to the surface of the cell.Completely break-down cells that have died (autolysis)

In general, the functions of lysosomes involve breaking-down i.e. processing to 'make safe' or make use of, or removing from the cell e.g. by exocytosis, useless and potentially harmful materials such as old worn-out parts of the cell or potential threats such bacteria. Lysosomes can therefore be thought of as the rubbish disposal units within cell