Whenever there is something wrong in a cell, the lysosome will digesting the cell itself, so that it doesn’t disrupt any of the other cells. However, an example of when this should happen in cancer. Why don’t lysosomes digest the cell then?
Cancer cells are a result of random mutations in your own cells. Usually cells with these mutations get caught immediately and are killed, but very rarely (in the case of cancer) their mutations make it possible to evade these death mechanisms (apoptosis, immune system detection) and multiply unimpeded in the body.
EDIT: In the case of lysosomes, they are the result of an intricate apoptosis pathway. If something in the apoptosis pathway mutates so that it no longer works, then anything afterwards - including lysosomes - would not get the signal to activate.
It’s likely that the cancer’s effect on the cell causes lysosomes to not be made at all, or the method which causes them to burst and self digest has also been interrupted.