What holds the overhead lockers?
The overhead bins are usually mounted to the aircraft structure. For example, in case of Boeing 737, they are mounted to the stingers using tie rods. From an accident report of Boeing 737-400:


  The forward inertial load is reacted by a diagonal tie, mounted at one end to stringer 6 or 7 in the fuselage crown and at the other end to a fitting on the upper surface of the bin. The vertical and lateral loads are reacted by short tie rods attached to the fuselage.




B737-400 overhead bin attachment. Image from the same report.