After your first Full Moon Operation (5/9) in Persona 3 Reload, you'll be able to start accepting Requests from Elizabeth from 5/10 onwards. These are all optional, but the rewards make them worth doing. You'll often need to complete one Request to unlock another, and some even have deadlines that you'll want to watch out for. One of the earlier Requests that you can accept is "Request 7: Bring me a Juzumaru."