Sylvia Plath led a complex existence, culminating in her suicide. Her poems contain depths that may escape the average reader but which contain her attempt to rationalize her being. Her seemingly normal childhood, without incident and her high academic merit were not enough to ensure a normal adulthood for her.
Mirror is an honest attempt to expose inner conflict in all people. What you see is not always what you expected or what you want and Mirror reveals how we are always seeking more, never content. The woman in the poem is "Searching my reaches for what she really is." She no longer recognizes herself. The figurative meaning attached to the "lake" is the seemingly bottomless reaches of a lake and the woman has apparently lost her youth, never to be recovered. The woman is looking intently in case she missed something and then, as if not satisfied with the fact that the mirror is "not cruel, only truthful" she seeks a different view of herself in "those liars, the candles or the moon."
A lake ripples and is constant whereas the moon or a candle cast shadows and create illusions that maybe do not exist - hence "liars." They cast a better view and hide the woman's real appearance.
The metaphor of the lake is extended when Plath adds "In me she has drowned a young girl." It reveals the finality of the loss of the woman's youthful appearance. The comparison is unkind as the woman is now "an old woman ....like a terrible fish." Although this is itself a simile ("...like a... fish") it is again extending the lake concept and the woman's seemingly "drowned" reality - her lost youth.