"I am important to her" (15)
The lake is telling us in plain words that it is important to the woman. Of course, she could have some sentimental attachment to the lake in general, but in this poem, the reason why she goes to the lake is to look at her reflection. So, we can make the connection that if the lake is important, her appearance is important to her. Dissatisfaction with her appearance, then, would explain her distress earlier in the poem.
In me she has drowned a young girl, and in me an old woman Rises toward her day after day, like a terrible fish (17-18)
The woman's fears of aging, and the sorrow she feels over her lost youth, have become physical through the metaphor of drowning and rising in the lake. These two lines are scary – not only has a young girl drowned, but a scary fish is also rising from the depths of the lake. Through watching herself in these waters, the woman has seen what she used to look like, and be – a young girl – die, while what she is becoming – and old woman – is rising up to meet her. We all know, at some level, that we are becoming older, but by watching herself in the lake, the woman knows this on a visual level, made more vivid by the image of drowning and rising in the waters.