There is paid luggage storage at Union Station, which is relatively close to the Capitol, if you want an alternative to hoping for a friendly bellman. It's not cheap, though.
We are planning to visit the capitol, white house, Lincoln memorial and have lunch in that area and leave capitol hill area
The White House and the Lincoln Memorial are miles from Capitol Hill, which refers to the neighborhood
east of the U.S. Capitol. The closest restaurants to the Lincoln Memorial are about a mile away in Foggy Bottom. (There are reasonable lunch options near the White House.)
Also, when you say "visit" the White House, do you mean admiring it from outside or actually visit it? Arranging a tour is complicated, and if you want one you should start the application process today. Go through your member of Congress.