National Park Service
The National Parks Service National Mall and Memorial Parks Division of Permit Management and US Park Police oversee permitting and demonstrations on National Park Service facilities in the Capitol Region. NPS regulations indicate that permits are required for events involving more than 25 people.
The Division of Permit Management office is incredibly understaffed so they are often very slow to respond to permit applications. For smaller events in some of the less trafficked parks (Stanton Park, Farragut Square, etc.), NPS staff will often just issue a permit via email without any further follow up. For permits in the more heavily trafficked areas and for larger events NPS staff will require a detailed site map and event plan to ensure compliance with their hundreds of pages of regulations.
The National Capital Area Event Planning Guide is a good tool for navigating the numerous rules and regulations governing permitting for events in NPS parks. Pay close attention to the sections on protecting grass and avoiding drip lines from trees – NPS is VERY serious about protecting their grass.
Lafayette Square and the White House
Probably the most restrictive space for holding protests in Washington, DC is in Lafayette Square in front of the White House. If you apply for an NPS permit for Lafayette Square you should expect a very rigorous review of your permit application and a very slow turnaround time on actually receiving your permit. Additionally, you will need to arrange with the National Parks Service and US Secret Service to screen all of your equipment on H St. before moving into the park and if you bring any equipment that was not on your approved equipment list it will not be allowed into the park.
A possible alternative for many smaller events with a more limited setup would be to apply for a permit from the DC Metropolitan Police Department for the stretch of Pennsylvania Ave, NW between 15th and 17th St. in front of the White House. This actually gets you closer to the White House and allows for a much more streamlined permitting process.