What does your lease agreement say about subletting? There is no inherent right to sublet--the lease itself controls. Most lease agreements give LL right of refusal--which your LL has now apparently exercised. Your situation will turn on the plain language of your lease. Bear in mind if LL refuses to allow another roommate you MAY be required to come up with the full amount of rent or face eviction.
If you want chapter and verse on the law you'll have to hire an attorney. Most (if not all) of it can be found online--the DC bar has links for landlord tenant laws in DC.
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