At the time of launch what was the air pressure in the Apollo LM, and the spacecraft-LEM adapter section (SLA)? Was the air vented from the SLA as the vehicle entered orbit?
I was able to answer this by taking some pictures of the Saturn V displayed at Johnson Space Center. Despite my skepticism, it is a real Spacecraft Launch Adapter (SLA), just as the Field Guide to American Spacecraft states.
We can see what are clearly a number of vents inside the SLA. (the crossed brace is not flight hardware, it merely supports the aft end of the SLA for display).
A closeup of one of the vents
The outside of the vents on this SLA are covered with metal disks because it was displayed outside for many years. But knowing what to look for, we can see the vents on a stacked Saturn on the pad.
As far as the Lunar Module (LEM) goes, we know that operationally it had a ~ 5 psi pure oxygen atmosphere. It's inconceivable that the light weight LEM structure could have withstood 10 psi crush loads, so the LEM must have been pressurized to 14.7 psi on the pad with pure O2, which then bled down through the positive pressure relief valves during ascent.
Reference (page 3-58)