B737 Captain reported an aft lavatory door malfunction led to a passenger getting trapped inside while the aircraft was going through weather and turbulence but cabin crew were able to open the door after landing.

Narrative

ZZZ1 - ZZZ. Passengers were greeted and briefed by me at the podium at Gate XX that all indications were that the flight was going to be turbulent and that the seatbelt sign would probably be on the entire way. When I made the Captain's announcement during boarding using the FA interphone and standing between seats in the first row I again reminded our customers that I expected turbulent conditions and that the seatbelt sign would probably be on the entire flight. The actual flight conditions were indeed turbulent. Seatbelt sign was on from brake set to brake release.The Purser informed me that a female passenger was stuck in the aft lavatory with approximately one hour remaining. As is my custom; periodically throughout the flight I ask the Purser how the passengers are behaving. This flight was no different and the report was positive. However; upon hearing this; I asked the FA multiple times if she thought this was some kind of scam or trick. All indications were that it was not. After multiple frustrating attempts (over approximately 30 minutes) to extricate her by all FAs I told the Purser to seek out; an able-bodied passenger to help them put pressure on the door hinges/latch/joint etc. to try to get her out. All of our weather products: TAF; ATC; ATIS; SIGMETs; Flight Plan Guidance (FPGs); PIREPs; indicated a turbulent descent all the way to landing (I have personally executed an Enhanced Predictive Wind Shear (EPWS) directed wind shear escape maneuver near FAF at ZZZ in the past under similar conditions). I was very concerned with her physical safety with regard to the stress she was under and the possibility of a catastrophic health event (stroke; heart attack; etc.) while also out of reach of first aid and/or turbulence that could result in severe head/spine injury. We had tried multiple altitude changes and heading vectors to alleviate the turbulence to no avail.I was the Captain and the pilot monitoring. I consulted with the crew and then directed that we attempt to use cockpit emergency equipment (the metal protrusion on the cockpit crash axe) as a pry bar to put pressure/leverage on the door hinge/latch/joint in an attempt to extricate her so she can be seated and belted in for what was expected to be a turbulent ride all the way to touchdown. It was my decision. The crew agreed that at no time would anyone try to break down the door because of the risk of injury. The emergency equipment was to be used solely as a pry bar / to increase our leverage/pressure on the door latch/hinge/joints. I set up the restroom break with a Purser. She concealed the emergency equipment in a plastic trash bag. I sat back in my control seat. We closed the door and the Purser walked to the back of the plane in one last attempt - it did not work. The Purser then put the emergency equipment back in the plastic trash bag to conceal it and walked back to the flight deck; we set up another bathroom break; she passed it to me and I re-stowed it back in its normal position on the flight deck. At some point during the process to extricate the woman the able-bodied passenger (good Samaritan) cut his hand - it was reported to me that it was not severe but that he needed a paramedic (he was treated upon landing by paramedics and seemed appreciative at the care we showed for the woman and himself). The Purser tried to offer reassurances to the woman by communicating with her through the vent near the floor of the door that they were able to remove. Approaching 10;000 feet and in the vicinity of multiple thunderstorms; I instructed everyone to take their seats and fasten their seatbelts and concluded my coordination with Dispatch with regard to the need of fire department/paramedics to meet us at the gate. I did my best to keep my First Officer (FO) as informed as much as possible. He did an outstanding job flying the plane and working the radio through the descent and executing a smooth landing.After clearing the runway; the Purser informed me that after landing the door opened (I can only assume it was due to pressure equalization). After some brief coordination with the Purser we asked ATC and received expedited taxi to [Gate] XY. Fire department and paramedics were there. I briefly talked with the passenger/woman in question. She was clearly shaken and visibly shaking and informed me that she was ok but had high blood pressure. She appeared grateful for our care and attempts to extricate her. The fire department looked her over and; I believe a Company employee escorted her to her new gate for her connecting flight to ZZZ2. I have never heard/read about this scenario happening in my career as a pilot. In my mind; the risk of severe injury to the passenger due to turbulence; wind shear; a blown tire; a collapsed landing gear; runway excursion; etc. warranted my decisions and our collective actions. I strongly commend the actions of my FO; my Purser; all of our FAs; the able-body assistance; and the passenger in question; for their calm; methodical; professional; and decorous behavior.