If you lean on someone is to rely on them for support, physical or moral. Informally, it can also mean "to exert pressure," especially if you're a mobster.
If you’re tired, lean against the wall. If you’re broke, lean on your family for financial help. But something can lean all by itself, if it’s not standing straight. The famous Tower of Pisa leans at an angle of about 4 degrees. As an adjective, we use lean to describe something skimpy or lacking excess flesh. When you're experiencing financial difficulty, you could say you're going through lean (not prosperous) times.