The purpose of lysosomes in a cell is to aid in the digestion and waste removal processes. Lysosomes are membrane-bound organelles that contain hydrolytic enzymes capable of breaking down various biomolecules, such as proteins, lipids, and carbohydrates. They play a critical role in cellular homeostasis by recycling cellular components and breaking down worn-out cellular structures. This function is essential for maintaining the cell's overall health and preventing the accumulation of harmful materials.