How do the hanging wall and footwall move in a lateral fault?

This is true of normal faults. In thrust or reverse faults, the hanging wall moves up relative to the footwall and in strike slip faults, it moves horizontally relative to the footwall.

This is a normal fault.

A normal fault is a fault in which the hanging wall has moved downward relative to the footwall.

Astrike-slip fault it when the hanging wall and the footwall slide past each other.

It is called a Normal Fault.