A lake is a type of mirror in that it also reflects images. You are correct though that the mirror and lake are metaphors for something else. They are ways of looking at (or perceiving) the self. In the first part of the poem, the literal mirror only reveals or reflects the truth (no bias, judgement, etc.). The lake, however, is more involved in the woman's self-perception. One could also say that it is only by exploring the outside world and nature (the lake) that we truly learn about ourselves. When we see ourselves every single day in the mirror we don't notice change quite as much. Or one could argue that we don't bother with introspection on a daily basis. It takes going outside or far away to truly learn about the self. This is just one observation; I'm sure other people might have other theories about the deeper or other more complex meanings of the poem.
