A reversible mortise lock for a storm door has a body, a latchbolt and an operational set. The body has two sidewalls, an actuator and a lock body plate. The latchbolt is connected to the actuator between the sidewalls and the lock body plate and has a connecting rod, a bolt head and a first spring. The connecting rod is connected to the actuator. The bolt head is mounted on the connecting rod and extends to the lock body plate. The first spring is mounted around the connecting rod. The operating set is movably connected to the body and the latchbolt and has an engaging panel and a second spring. The engaging panel is movably mounted between the sidewalls, is mounted around and selectively engages the connecting rod and has multiple pushing levers, a through hole and an engaging protrusion. The second spring is mounted on the engaging panel.