Question

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

Answer 1

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

Answer 2

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