It's actually more common to say the opposite 'to lean towards doing something' meaning you are likely to decide to do it - I'm not sure if I've actually heard it used as 'leaning away' but its obvious what it would mean.

"To lean against" is not a synonym, but rather a phrase that means "being partial to" or "thinking of doing." If someone says he/she is "leaning against" doing something, he/she is almost deciding not to do the said action.