I want to strengthen a lazy eye by wearing only 1 contact lens. Which eye should I put it on?

Weaker eye. The goal of strengthening a lazy eye is to make the vision equal to the best potential in both eyes, which means correcting both to 20/20, and sometimes we cover the stronger eye to make the weaker eye be used more.
Depends. If the weaker eye is blurred then the lens should go on that eye. If both eyes are blurred then possibly both eyes may need lenses. The goal is to improve the image in the weaker eye with lenses and in rare cases to weaken the correction temporarily in the better seeing eye to force the weaker eye to be used.