Lethal injection is a special way grown-ups use to make someone really sick so they become sleepy and never wake up again. It is like when you feel tired, close your eyes, and go to sleep, but this time it happens forever.
Doctors give the sick-making medicine to the grown-up who is going to sleep, and they do it in special places where nobody else can see it happen. They put a needle in the grown-up's skin, usually in their arm or hand, and slowly drip the medicine inside the body through the needle.
Lethal injection is just used when a very grown-up person is getting into really big trouble because they did something very bad, like hurt other people in a very bad way. Sometimes, the grown-up who did bad things ask to go to sleep forever because they don't want to live anymore.
But even if it may look like a nice way to go to sleep, some people don't like lethal injection because it can still hurt the grown-up when they put in the needle. That is why others are trying to find new and less painful ways to help people go to sleep forever.