"What lips my lips have kissed, and where, and why" is an Italian sonnet. The first stanza of these kinds of sonnets establishes the speaker's "problem," which is traditionally the problem of love, particularly unrequited love.
The first line of the poem fulfills the reader's expectations for an Italian sonnet by bringing up the speaker's past experiences of love. The speaker wonders about the lips she has kissed, where she has kissed them, and the emotional reasons for kissing them. Note that "lips" here is an example of synecdoche, as these "lips" refer to the speaker's past lovers.
The alliteration of the /w/ sounds in line 1 force the reader to slow down and focus on these questions of "what," "where," and "why" that the speaker is asking. The repetition of the coordinating conjunction of "and"—an example of polysyndeton—further slows down the reading of the line, as does the end-stop at the end of line 1. The end-stop enhances the surprise of line 2, the beginning of which transforms line 1 from a series of questions to a declaration—there will never be an answer to these questions of "what," "where," and "why."
In the beginning of the second line, the speaker declares she has forgotten all her previous experiences of love. Thus, in a departure from traditional Italian sonnets, the speaker's problem is not that she is experiencing unrequited love; rather, it is that she has forgotten all her loves of the past. The caesura after "forgotten" creates a brusque ending to the phrase "I have forgotten," reflecting the harshness of the sentiment. The caesura also emphasizes the importance of the phrase by setting it apart from other words in the line.
The use of synecdoche in using "lips" to refer to the speaker's lovers heightens the speaker's sense of detachment from her memories. These lips are disembodied and unattached to individual faces, names, or bodies. They tease the speaker's memory, but provide no real information or context. All they can accomplish is remind the speaker of the meaningful, pleasurable, and comforting memories she has lost. Furthermore, the use of diacope in the repetition of the word "lips" heightens focus on the imagery of the lips--a reminder for the speaker of what she once had and now has lost. The repetition of the coordinating conjunction of "and"--an example of polysyndeton--further slows down the reading of the line.