How does lymphoma lead to death?

Uncontrolled growth: Lymphoma cells continue to divide and grow more than they die. Two things happen 1) their increasing size affects normal organ function or physically pushes on organs which impair their function or 2) they produce substances that are toxic or debilitate the patient both these things eventually weaken the patient, prevent the production of normal blood cells and can lead poor immunity & infection.

Like other cancers: Lymphoma can infiltrate critical organs and cause them to fail. Treatment and the disease itself can obliterate bone marrow elements leading to infection, bleeding and death.