Die in the LM when the oxygen runs out, die in orbit when the PLS oxygen runs out
I think I kept seeing 4 hours given as the PLSS lifetime, but that seemed rather short. The J missions were regularly pushing 8 hours on each PLSS charge, and that didn't count the OPS. Although the OPS would only last 30-60 min when used in the simple scuba-like once-through mode it was designed for, it actually contained quite a bit of oxygen and could conceivably supplement the PLSS tank for quite some time.
The problem then would be the limited supplies of LiOH, H2O and battery power. In some usage scenarios these were more limiting than O2. In principle you can do without LiOH entirely, but only by wasting a lot of O2 because you would then have to dump a lot of it to get rid of the CO2 before it built to dangerous levels. I think the ISS CO2 scrubber uses a material that can be regenerated by exposure to space where it gives off its CO2.
By minimizing your physical activity and turning off the radios you could extend all of those consumables. And in principle you could supplement some or all of them with supplies on the LESS itself.
Seems to me it shouldn't be that difficult to get into the correct orbital plane. Just use lunar landmarks for left-right steering.
Problems with visual flying would start at liftoff. You would need a notable landmark visible from your location that had been calculated to be more or less on the intended flight path. Then once you were up and past that landmark further navigation would rely on being able to recognize other landmarks from the "air." Not an easy task for an unpracticed flight. They practiced landmark recognition for the landing zone but had a specified flight path and a simulator. Flying by hand over an ad hoc flight path trying to reach altitude and inclination marks while simultaneously navigating by sight over unfamiliar terrain would seem to be a unbelievably difficult.
I suppose that if you were able to get visual sighting of the CSM early enough then the crew could use the visual rendezvous procedures developed during the Gemini missions. It would be interesting to read a full flight plan.
For those who wish to maintain an illusion, ignorance is the best source of knowledge.
I seem to recall that running out of PLSS cooling water during a lunar EVA was a huge concern.
It was. The J missions carried extra supplies and you'd often hear Houston warning the astronauts to expect a "feedwater tone" in a few minutes.
Spacesuit thermal control is very challenging. You'd think it shouldn't be that hard to dump metabolic heat when you're nearly surrounded by the blackness of deep space. But the numbers change a lot. You might generate anywhere from less than 100W when sleeping to over 500W working very hard. You might be exposed to sunlight at 1.4 kW/m^2, or you might be in the shade. You might be doing an EVA in deep space or working on the lunar surface, whose temperature might vary from 100K at night to 390K at noon.
As I can figure it out, the design philosophy is to insulate the astronaut from the variability of the external environment and then actively remove his metabolic heat by cooling the oxygen gas flow or with combined gas and liquid cooling.
But it's difficult to radiate hundreds of watts at body temperature from something as small as a backpack. Water is a very handy coolant because it has a high heat of vaporization, and it vaporizes spontaneously in a vacuum. Unfortunately water is an extremely scarce and valuable substance on the moon, at least in the equatorial regions explored by Apollo. So while water sublimation worked well for Apollo it is completely impractical for any kind of long term lunar base unless water can be easily mined in large quantities from the polar regions.
Even so, water seems like too valuable a substance to be used for something as pedestrian as cooling. I think a totally different approach will be needed. I've seen studies of an interesting approach that uses hydrides. Many reactions with hydrogen are either exothermic or endothermic, and a lot of NiMH battery research has been to find materials that are thermodynamically neutral when they give up or absorb hydrogen. But if you can find two very dissimilar hydrides you might be able to make a reusable cooling unit that can be "recharged" between EVAs without spending any water or other consumable.