Bumps
Although they do occur, cancerous lumps in the foot are rare. Some lumps are made of non-bony soft tissue. Depending on what type of lump it is, it might be reasonable to remove it or better to leave it alone unless very troublesome. In particular, lumps on the sole of the foot should be treated with caution since the scar can be sore to walk on after removal and the lump itself can return. Hard lumps on the top of the foot or base of the great toe are often "spurs" at the edge of an arthritic joint and are made much larger by the pad of tissue which develops to protect the area from shoe friction.
Despite the arthritic change, the joint itself might not feel painful at all so that only the bumps need be treated (by removal). Alternatively, examination might reveal the joint to be causing some of the pain and treatment must then address both bump and joint to be successful.