Potassium chloride is supposed to stop the heart, at which point one ought to lose consciousness anyway. All pain ought to stop seconds after the heart stops. As a friend of mine once said "drop like a sack of potatoes". Even before death.
The lethal injection protocol, of which there are many, also calls for a barbiturate, often Nembutal, but the dose is lower than used in euthanasia and its just meant to induce a loss of consciousness and let the potassium chloride do the actual killing. Again, once the heart stops the other drugs make no difference. You can also be rendered unconscious by taking a heavy dose of Xanax. Xanax is no Nembutal but it will put you to sleep, it just wont cause respiratory depression like Nembutal does.