Can a skin cancer lump leak small amounts of blood and pus?

It is possible. It is possible. Best to bring this lesion to the attention of your friendly dermatologist.
Unusual. This sounds more like a sebaceous cyst then it does skin cancer. Certain types of skin cancers when they get large can get infected and can have drainage of blood and pus. You should have a complete physical exam to figure out the reason for this drainage.