What does the narrator learn by looking into the looking glass in The Lady in he Looking Glass? 

The narrator learns that she is alone and everything she portrays is a facade she can best be described as empty. The narrator's home is viewed through the looking glass.

Explanation:

"in The Lady In The looking Glass" by Virginia Wolf, The unnamed narrator can be inferred to be Isabella because she is seen as a reflection. The narrator describes the lady's room showing how richly decorated it is, although she has not paid the bills. on the surface Isabella appears to have everything whereas she is lonely and empty.

Their is a void in the Isabella's life, although she has the finest of cloth and the best best of furniture, but she has no friends nor companion. her richly decorated room is showing through the mirror but deep down Isabella is living her life as a facade.

Are you sure you wrote the correct question/sentence? or is this maybe a trick question? there are no relative pronouns in this sentence. there are two pronouns here:   she  (personal pronoun) and  that  (demonstrative pronoun). although  that  can sometimes be used as a relative pronoun (this is the cat  that  i petted), it is not the case here.