Lysosomes usually digest macro-molecules that somehow get through the plasma membrane. macro-molecules are also called as "big" molecules or foreign matter, like bacteria or non-functional organelles. plant cells don't really have that problem, because the plant cells have cell walls.
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animal cells have lysosomes

==> they need to digest dead cells
==>they need to digest bacteria or other harmful substances which enter the cell
==>animal cells do not have semi permiable membrane
==>dead cells in animals effect their health so they need to be replaced
==>lysosomes are very important for animals

plants do not have lysosomes

==>they have semi permeable membrane
==>harmful things cannot enter plant cells
==>dead cells help plants in one way or the other so they need not be replaced -- eg -->parenchyma 
==> therefore lysosomes are not needed in plants

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