Russell Bucklew wakes up most mornings with blood on his face.

Due to a rare health condition, he has trouble breathing when he lies down. So he sleeps at a 45-degree angle, elevated by pillows, to try to avoid choking and hemorrhaging. But blood still usually leaks from his mouth and nose.

That bleak reality, along with compromised veins, sensitive tumors, and other maladies will produce a “gruesome and predictably excruciating death” if Missouri executes him by lethal injection, Bucklew warns the U.S. Supreme Court ahead of Nov. 6 oral arguments.

Lethal gas would be less brutal and closer to...