Air carrier flight crew reported a water leak in the lavatory in cruise flight.

Narrative

Climbing out of ZZZ at approx FL200 got a call from the Purser saying that water was leaking/streaming out of a hole" in the lav floor. After further discussion she explained it was a vent hole on the floor of the lav below the toilet. I advised her to keep an eye on it and to use a blanket to wipe/absorb the water. Once reaching cruise altitude I called back to the purser and she said the leak was still occurring and that she had used X blankets and they were soaked already. At this point a clear division of responsibility was established and the FO managed the flying and ATC. There was no guidance provided in the QRH (Quick Reference Handbook). I did confirm that it appeared to only be water. Water was now leaking out of the lav under the FA'S jump seats and into first class. We used ARINC to contact dispatch and patch in an airframe mechanic. After explaining the circumstances the mechanic asked to have both shut off valves in the lav turned to off. After monitoring the leak for approx. XX min it did not subside. At this point we were approaching ZZZ2. With input from maintenance control and dispatch the decision was made to divert to ZZZ1 with approx. 1.5 hours of flight time to ZZZ1. Factors taken into consideration for a divert were: 1. Concerns about possible water intrusion into the E&E compartment although unlikely according to maintenance control. 2. Possible water freezing on control cables and having a possible effect on flight controls (as explained in the FM X.XX.XX). Contract maintenance in ZZZ2 with limited access to parts which may strand the aircraft there if a significant issue is found.At this point I had a discussion with the FO about the situation and the decision to not [request priority handling] but to plan a mechanical divert into ZZZ1. We discussed the importance of possible electronic and control issues and that if any indications became apparent; we would re-asses our situation declare an emergency and divert to a closer airport as necessary. We also discussed the significance of being over weight for landing; that it was not a primary concern and we would manage that once we had a revised flight plan. ATC was notified of the divert and new routing was provided to ZZZ1. Dispatch updated the release to show ZZZ1 as the new destination and we received and reviewed a new flight plan. The diversion planning guide (FOM) was reviewed. An ELB (Electronic Log Book) report was sent. Per the Flight plan and on board calculations confirmed we would be approx. XXXX lbs overweight. Since it was non emergency; we chose to descend to below FL180 to continue the flight and this got us approx at landing weigh (+300lbs). By further managing drag devices within limitations we were able to ensure a landing below MLW. Just for clarification; we did discuss the fact that an overweight landing is not a major concern in circumstances where an urgent situation arises or plans change but since it was manageable to avoid one we would mitigate it as best we could. (If the need to divert to a closer airport became necessary because of issues mentioned above we would execute an overweight landing). On arrival into ZZZ1 a short debrief was completed at the gate because of the need to swap ac. (We completed a much more thorough debrief on our subsequent flight). We arrived in ZZZ1 at XA:36; equipment swap and departed at XB:24."