Such cells where the lysosome bursts, will die and here is how it occurs.
Lysosomes are tiny bags covered in membrane and they are found in the nucleus of a cell. On the inside, lysosomes carry powerful digestive enzymes with which they digest materials that are found in the cell. They have in them acid hydrolases and other enzymes that can digest organelles when they are either in excess or when they are worn out. The lysosome also digests engulfed bacteria and viruses, food, and other macromolecules
So, should one of these bags burst open or rupture within the cell, it will lead to something called autolysis. That is, the enzymes present in the lysosome will digest the cell of such an organism along with other parts of the cell. When this happens, the cell is left damaged or digested which will lead to the death of such cells.