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.