I’m really not sure legally if you’re supposed to have a license as it stands right now, but I know that with the proposed updates, you will. They’re not as stringent if you’re living there versus if you’re renting an entire property out and not living there.
Proposed: http://1.usa.gov/Jifswt (DCRA–under Related Documents)
Either way, yes, you should absolutely have a lease. You need it in writing that the people who are living with you have agreed to pay you rent, and how much, and for how long. Here is a sample DC realtor lease: http://www.evarealty.com/Rental_Forms/Lease_Agreement.pdf