Yeah, but “on death’s door” gives me the sense of a man too ill to effect revenge or anything else beside popping pills. Whereas “terminally ill” conveys to me the sense that the clock is ticking; he’s under a death sentence to die soon, albeit at an unspecified date. He’s healthy enough to begin with but in a race against time.

As with Walter White in “Breaking Bad”. His diagnosis constitutes a death sentence — but the date is uncertain and he’s initially healthy enough to carry out his plan to earn enough money for his family by cooking meth.