How is the quote, "lend me your ears" an example of a synecdoche?
It is a figure of speech.
Synecdoche is a figure of speech where a part of something is used for the whole or vice versa. Therefore lend me your ears is a synecdoche because in lending the ears the person is using part of the body to give the person making the statement his/her full attention. So the ears act for the whole body.