According to this question, it is forbidden to lean on anything while praying the amidah, where leaning means the object bears some of your weight. What does somebody who can stand but only with the aid of a cane, walker, or crutches do? I have heard (no source) that somebody who can't stand at all prays while sitting; does the person who can't stand unaided sit, or stand and lean?
The most famous leaning in Judaism that I can think of is during the Passover Seder. There we lean to show that we are wealthy and like kings. Wouldn't it be that when Davening shmone Esre we are humbling ourselves before Hashem and therefore don't want to appear as wealthy or like kings? Following this logic, people who must have something to lean on would not be held to this same standard as they are not appearing as kings and are still humble in the eyes of Hashem.