[slg]

I'm unclear on what you are correcting. I didn't state he was the first to do a lunar orbit in his own spacecraft, but he was the first to do it without any other nearby craft. As far as I'm aware, the lunar module and the command module were never actually that far apart during Apollo 10. So while they were separated, the distance between the two was measured in hundreds of miles rather than the thousands of miles that was true during Apollo 11 and the later lunar landings.

[gshubert17]

Some mission parameters are at: https://en.wikipedia.org/wiki/Apollo_10#Mission_parameters

The lunar orbit of the LM (Lunar Module) and CSM (Command-Service Module) had a period of 2.15 hours. The interval during which the LM orbited separately from the CSM was 8 hours 10 minutes, or about 3.8 orbits. Thus, at times both craft would have been on the far side of the moon. While the LM was in its lower orbit I don't know how much shorter its orbital period would have been, or whether it "lapped" the CSM during the time between closest approach and redocking.