I pasted from the Smithsonian below (link below that). Another link at bottom for responses to same question on Trip Advisor. Good luck and enjoy DC!
Checkrooms/Lockers*
Lockers are subject to CLOSE WITHOUT NOTICE. Security requires all bags be inspected before they can be placed in self-service checkrooms or lockers. Lockers are for the use of museum patrons only while they visit the Smithsonian.
Lockers are available as follows:
•African Art Museum – lockers with keys
•American History Museum – lockers with keys
(various sizes) on 1st floor (Constitution Ave)
•Freer Gallery and Sackler – lockers with code lock
•Hirshhorn Museum – lockers with code lock
•Natural History Museum – lockers with keys (Const. Ave. & Mall)
•Postal Museum – lockers with keys
•Reynolds Center for Art & Portraiture – lockers with digital locks (F & G Streets)
•Udvar-Hazy Center – lockers with keys
BAG LUNCHES, properly closed and secured, can be stored at these facilities.
*Most lockers are appropriate for coats, small bags, and carry-on luggage.
Alternate non-Smithsonian location:
Union Station luggage storage room
6 a.m. – 10 p.m. daily
charge determined by size of bag & length of time
open to public (not just rail passengers)
need photo ID
Security and Policies | Visit | Smithsonian
Taking suitcases to the Smithsonian - Washington DC Forum - TripAdvisor