I had an epidural shot in my back a couple of days ago because of degenerated discs and associated pain. First, they set up an IV. Once in the procedure room - death chamber in this analogy - the nurse injected versed into the tubing as a calming drug. Then when the doctor came in to do the shot, he injected lidocaine so the propofol would not burn when it was injected. Propofol puts you to sleep, even though they say it's not "deep sleep", but for me I never know what's happening until I wake up 10-15 minutes later. After the propofol, he injected the steroid cocktail for pain.
So why don't they follow this type of procedure, but instead of the steroid, they inject the lethal drug while you're zonked from the propofol? You'd never know what happened. It's certainly painless. When the propofol hits, it's actually very pleasant.