The poem appears to contest your assertion that
an object can not both be a mirror and a lake.
Its title is Mirror, not Mirror and Lake. Throughout the poem, the speaker is the mirror. But in the second verse, the mirror claims to be a lake. What does this mean? It's easy to see how a lake can be a mirror, since it reflects. But how can a mirror be a lake? Let's unpack the poem and see.
The first verse stresses the objectivity of the mirror:
I am silver and exact. I have no preconceptions.
The mirror insists upon its truthfulness and its emotional detachment:
... unmisted by love or dislike.
I am not cruel, only truthful‚
The eye of a little god, four-cornered.
The mirror claims to be as indifferent to human concerns as any Greek god. Even as a lake, the mirror says that when the woman looking at her reflection turns away,
I see her back, and reflect it faithfully.
Throughout, then, there is an assertion of precision and exactitude. Yet the mirror is not merely a passive observer. Its claims to neutrality are undercut by its reference to its "heart". Furthermore, it is active:
Whatever I see I swallow immediately
Just as it is
Already, then, in the first verse itself the mirror is a bit like a lake. A lake swallows anything you put into it, and the mirror swallows everything it reflects. A person who has been swallowed by a lake is, of course, drowned. So also the ageing woman has drowned her younger self in the mirror:
In me she has drowned a young girl, and in me an old woman
Rises toward her day after day, like a terrible fish.
The point here is that although we think of mirrors as neutral and exact, they are freighted with emotion, because of the response we have to them. There's a similarity here to existentialism or absurdism: the world itself may be meaningless and indifferent, but we find ourselves forced to make meaning of it. The mirror itself claims objectivity, but it is no more objective than a lake.
We think of a lake as part of the natural world, as something that is beautiful; but a lake can be cruel even as it is beautiful, or as it reflects beauty (think of Narcissus, pining away for his beautiful reflection in a lake). We think of a mirror as something manufactured, something relatively objective and passive. But Plath shows that the mirror and the lake are one and the same: parts of a non-human world that is indifferent to human feelings, and thus cruel.
Ageing is part of the natural world too, and part of its cruelty. If the poem can be boiled down to a single "meaning" (which it shouldn't be), it is that the world we live in is hostile and cruel even as it claims to be neutral, and that we are all subject to its indifferent, remorseless cruelty.