If the lethal injection drugs are administered correctly the person being put to death by lethal injection is usually dead within a few minutes once the final lethal injection drug is introduced.
The person being put to death is put to sleep first so that they are sleeping and then a second drug is sent through their vein that stops their heart.
Then once their heart stops beating they are usually dead but they have to be pronounced dead.
In most cases a person who dies of lethal injection is dead within 2 to 7 minutes after their heart stops but sometimes it can take as long as 2 hours for the person to be put to death if they cannot find a suitable vein.
But most times a person is put to death and dies within a few minutes of having the lethal injection done to them.