The assumption, in every risk analysis I’ve ever seen, was that if something broke, it would be the Lunar Excursion Module. After all, all the Command and Service Module systems would have a good workout before even approaching the moon, and the LEM was small and somewhat flimsy.

The assumption I’ve always read about is that if the ascent engine failed to get the LEM back up to the proper orbit, or if it did but something went haywire and the LEM couldn’t dock, the CSM would complete the recovery—if necessary, dropping as much as about a third of the way down toward the surface.

But what if, after the LEM was on the moon, the CSM pilot died for whatever reason?

Well, if everything functioned correctly on the LEM, then yes, they could do it. Either spacecraft had the ability to rendezvous independently, and they each had the same computer and the ability to communicate with Earth.

It’s also possible that the CSM might could have been controlled from Earth (the LEM could be) but I’ve never run across any reference to this ability, and anyway, that certainly could not be used for docking. Only the CSM could perform an actual dock, if for no other reason than that it didn’t have a docking target (see below) and the LEM didn’t have the “upward” visibility needed for docking.

That’s okay, because they might not have been able to dock anyway. Both LEM hatches could be opened from the outside, but I’m not sure whether the CSM’s crew transfer hatch could be. Even if it could, in order to dock, the docking probe would have to have been installed and cocked before sealing the hatch and before the CSM pilot left this mortal coil. If all that was done and the LEM docked, when they opened their end of the tunnel, they’d see nothing but the narrow end of the aluminum drogue with no way to get past it.

If they somehow got past that without venting the spacecraft….no, they wouldn’t even try. Instead, they’d fall back on a procedure they had actually trained for: Extravehicular Crew Transfer. They would switch to their life support backpacks, go out through the other hatch (the one they used to descend the ladder to the moon), and climb over to the Command Module Crew Access Hatch.

That hatch could definitely be opened from the outside—but you need a special wrench. Did they have that wrench or some usable facsimile among their small cache of tools aboard the LEM? Probably, but I don’t know for sure.