answer to "Is Wesley the permanent captain of the Lexington
?" question in my mind is answered by the probable
answer to the question, "why is Wesley wearing a Starfleet Command patch?"
Since "The Omega Glory" was filmed after "The Ultimate Computer," and Bob Justman sent his now famous 'under penalty of death!' memo (basically saying "All starship members wear the same patch") to Bill Theiss on the 18th of Dec 67 ("The Ultimate Computer" finished shooting on the 14th), the answer can't be that Justman's memo influenced the selection. Even if Justman had clued Theiss in before he wrote the memo, wouldn't Theiss then have Wesley wearing the "starship arrowhead" patch?
Based on what we know from other episodes, I speculate that the "The Ultimate Computer" writing and/or production team consciously decided Wesley really worked for Starfleet Command and was given temporary command of the Lexington
just for this special
mission (I say special because nearly half of the starships in the fleet were involved!) and conveyed that to Theiss.
If that's not the case, why wouldn't Theiss have just assumed Wesley was
permanent captain and then created a unique Lexington
patch for Wesley's uniform, just like he had for Decker's Constellation
uniform (and would do just a week later for Tracey's and Dr. Carter's Exeter
It has been suggested perhaps the Lexington
crew wore the same patch as members of Starfleet Command. While I admit what I wrote above is all speculation, and I don't suggest my speculation is more insightful than anyone elses... that solution just seems too contrived for me based on what we see in all the other episodes that show non-Enterprise starship and Starfleet Command personnel.
As to what happened to the Lexington's
real captain? Maybe he was given temporary shore duty while the M-5 tests were carried out. Why not, we saw that play out--albeit under false pretenses--for "The Menagerie Part 1:"
SPOCK: This is First Officer Spock. Per Starfleet orders this date, I have been placed in temporary command of the Enterprise
. While our destination is secret, our mission is relatively simple. Starbase Command has assigned Captain Kirk medical rest leave until our return. His instructions are that you will obey my orders as you would his. First Officer out.
MCCOY: What's going on around here? Who said Jim needed a medical rest leave?
It's also possible the Lexington
was between captains... again, that's speculation... that and three dollars gets you a large coffee.