What was the mass of the Lunar Module cabin pressure vessel - that is, the metal structure that contained the astronauts, including windows and hatches, not including internal fittings and equipment, thermal insulation, or micrometeroid protection, and not including the astronauts.
You are unlikely to find this number (yes, I have looked), because that's not how the lunar module was designed or constructed.
Section 126.96.36.199 of the Apollo Program Summary Report describes the construction of the command module. The pressure vessel is a distinct layer that is constructed first. Then, a second phase of welding adds the longerons (the weight-bearing "frame"), equipment cabinets, and cold plates. After this second phase, the CM goes through a tumble-and-clean machine. The third phase is to install electrical, plumbing, and controls. At the end of each of these phases, the CM is weighed and tested for leaks. So, it's fairly easy to talk about the weight of the CM pressure vessel at any of these phases.
In contrast, the LM acsent stage was built in sections, not layers. The forward section contained the controls, displays, hatch to the lunar surface, and some cabin storage. It was where the astronauts stood during landing and take-off. Some sources call the forward section the "crew compartment"; this is a misleading name, as the crew also resided in the mid-section. The mid-section joined together the other two sections, and contained the docking tunnel, life support equipment, ascent engine, and more cabin storage; propellant tanks are mounted to the outside. The aft section was unpressurized (not part of the cabin) and contained equipment.
Each of these sections had their own design and manufacturing teams. The structural components and pressure vessel were integrated, rather than the distinct layers of the CM:
The combination of beams, bulkhead, and truss members forms a cradle around the cabin assembly; it takes up all the stress loads applied to the ascent stage.
Apollo Operations Handbook: Lunar Module, section 188.8.131.52
Controls, equipment, wiring, and plumbing were added as each section was built. Only once the sections were finished were they welded together, sealed, weighed, and tested for leaks. The thermal/micrometeoroid layer was added later.
So the LM pressure vessel was never designed, constructed, or weighed as a discrete layer.
While DrSheldon's answer is likely the most useful one, an upper limit of the materials forming the pressure wessel could be found by taking the mass of the LM ascent stage, and subtracting everything that isn't part of the pressure vessel. Unfortunately, accurate mass data for the parts isn't easy to find.
Dry mass is mass without propellant, but it's not clear whether this includes the onboard water and coolant as well (85lb (39kg) of water, 25lb (11kg) of ethylene glycol).
We do at least have data for one somewhat heavy component, the LM ascent engine at 180lb (82 kg).
There were also 250lb (113kg) of batteries.
So far, the upper limit is below 2,000kg.