As the previous educator already relates, this concept is presented by Joshua Rothman in an article called “Hamlet: A Love Story” where Rothman uses the exact wording from your question, saying we “love because we lack. Inside each of us there’s an emptiness.” The “emptiness” here indicates a void within each of us that cannot be filled. Hamlet, as a character, is a perfect example of someone who has this emptiness.
Hamlet's emptiness exists on many levels. First, Hamlet’s emptiness exists because of the death of his father. While he deals with this emptiness, he continues to love Ophelia. Hamlet’s emptiness continues when his mother immediately marries his uncle Claudius after Hamlet's father dies. Again, Hamlet clings to Ophelia. Later, Hamlet is presented with yet another “lack” of love, this time from Ophelia herself, when she spies on Hamlet for both Polonius and Claudius, ending her relationship with Hamlet in the process. This proves Hamlet’s void of emptiness can never be filled. Hamlet then decides to look insane. Many scholars believe Hamlet actually becomes insane in the process. In my opinion, the closest Hamlet gets to filling this void is through his platonic love for Horatio. Horatio wants to end his own life when Hamlet dies, but he vows to live in order to tell Hamlet’s story. At least this tragedy ends with a note of hope that, through friendship, our feelings of emptiness can begin to lessen.