It is the lysosome because it is the cell that contains digestive enzymes that can break down a dying cell into food.
The organelle that undergoes with autolysis is the lysosome. They are specialized vesicle that contain different digestive enzymes that involved with various cell processes such as breaking down excess cell parts that beyond repair, process damaged or dying cells and recycle worn out cell parts.
Moreover, lysosomes maybe used to destroy invading bacteria and viruses by digesting it or undergo a self-destruct mechanism.
Lysosomes. Autolysis is initiated by the cells' lysosomes releasing digestive enzymes into the cytoplasm. These enzymes are released due to the cessation of active processes in the cell, not as an active process.