Parked on the street.
I used a parking garage between the white house and Ford theater.
Parking downtown is hard. It's better to ride the metro. You can do like street parking on the National Mall bit it's parallel parking and very hard to do. Sometimes the spots are small. There isn't a parking lot dedicated to the lincoln memorial though.
I parked on the street across the park on the left. Paid parking. Looks like DC is trying to squeez every penny out of visitors. There are no free parking anywhere. There used to be a parking lot about half a mile south west of Tidal Basin, across from Potomac. They took over that also. If you get lucky, you can find free parking in between the two buildings of Library of congress.
Best to park on the National Mall. Madison Ave closest to the Monument is easy to park at any time. If you want closer, then Constitution Ave has plenty of parking
Ride metro, way easier.
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