Safe Storage Lockers for House Office Buildings Act This bill permits employees of the House of Representatives to bring certain weapons into House office buildings provided that the employees store the weapons in storage lockers operated by the U.S. Capitol Police. An employee who is authorized by the District of Columbia (DC) to carry self-defense spray, a stun gun, or a firearm may bring the weapon into a House office building if the employee (1) carries the weapon in a manner that complies with DC laws prior to entering the building, (2) enters the building through an external pedestrian entrance, (3) leaves the weapon in a storage locker while in the building, and (4) immediately exits the building after retrieving the weapon. The U.S. Capitol Police must install and operate storage lockers at the external pedestrian entrances of each House office building.