Lethal injection is a three drug cocktail. I seriously doubt that there is any pain involved given the order that the drugs are administered.
1. Sodium thiopental(aka Sodium Pentothal): is a rapid-onset short-acting barbiturate general anaesthetic. It is an intravenous ultra-short-acting barbiturate. In the
proper dosages it acts as an intoxicant similar to alcohol. Which is why it is known as "truth" serum in pop culture.
Lethal Injection dosage: 2-5 grams
2. Pancuronium bromide: is a typical non-depolarizing curare-mimetic muscle relaxant. This drug stops the breathing process.
Lethal Injection dosage: 100 milligrams
3. Potassium chloride: When used in lethal injection, bolus potassium injection affects the electrical conduction of heart muscle. Elevated potassium, or hyperkalemia,
causes the resting electrical potential of the heart muscle cells to be higher than normal. Without a negative resting potential, cardiac cells cannot
generate impulses that lead to contraction.
Lethal Injection dosage: 100 mEq (milliequivalents)
Personally I don't see how they can experience any pain. The Pentothal puts them to sleep extremely quickly and the other drugs stop the lung function and the heart function. They are asleep when all this is going on. Besides I think they should suffer some because they did something reprehensible to get sentenced to execution.