Yes indeed. It's this gentleman. Nice job, Henoch! All clues came from Season 3.
1. Hey, no one commented on my own disappearance.
Lemli accompanies the landing party to the planet in Wink of an Eye, and while Compton disappears, so does Lemli. Of course, it's only an offscreen, out-of-universe disappearance, but it is interesting given that Kirk later puts the ship on full security alert and we don't see Lemli again. We do see two other redshirts, of course - the ones who bang into the Scalosians' force field outside environmental engineering.
2. Let me demonstrate the awesome power of this device and put a new spin on the message?
In That Which Survives, Lemli, with only a word from Kirk to Spock, instantly unholsters his . . . Phaser Two (hint hint) and sends the Kalandan defense system into permanent hibernation. It spins a bit as it fails and, as far as the message, it is *not* That. Which. Survives.
3. Now this appearance just isn't very viable.
Lemli and Scotty are just illusions in The Empath, cooked up by the far more - ahem - viable Vians.
4. Maybe I should do something about this glowing thing . . . if only I were armed.
In And the Children Shall Lead, Lemli and Leslie just stand there, fully armed, as Gorgan materializes on the bridge right next to them and hangs around issuing threats. They may have already been under his influence, but they sure were casual about it. Where was Grant from Friday's Child when you needed him? I even checked on this year's prevailing usage of the subjunctive for you folks.
Incidentally Henoch correctly applied the answer to Clue Two to this one, and it works just as well or better.
5. Copy that, Yonada. No way? Way.
Copy that = Roger; Yonada = Hollow; Way. Lemli was played by Roger Holloway.
6. This instance of the game isn't confined to one segment, is it?
Just making sure no one was hunting for one episode that explained all of this.
7. Clearly, I must return to the posting of the first clue. In this outing, I vanish also, but no one seems to notice that changing of the guard, and when the one guy asks the other guy about certain reports, he's really only talking about me and someone the one guy could have asked directly, as well as the one guy and the other guy themselves. I mean, as far as we know.
This was my er, hollow attempt at an SPB-style clue. So we went back to Wink of Eye. I always found it interesting that when Kirk goes to sickbay for his exam, he asks McCoy if any of the "other men" reported anything strange. But he's really only talking about Spock and Lemli, because Compton is "gone," McCoy is standing right in front of him, and Kirk is the fifth and final member of the landing party. Of course, there could have been another scientist or security person whom we didn't see; the WOE landing party is a touch unusual (but not unheard of) in that we don't see it beam down or beam up. Anyway, Kirk could have asked Spock if he was feeling weird, so when he says "the other men," it just strikes me as unusual because he's pretty much only asking about Lemli, whose appearance in the episode is at an end.
8. In the same installment featured in Clue 4, thank goodness I was on escort assignment and not, say, on relief planet duty. I mean, that was no relief. Geez.
Thank goodness, in ATCSL, Lemli was shadowing one of the kids (Mary?), and wasn't assigned to "beam down" to Triacus, since, well, you know.
9. Clue Six does not refer to any on-screen event. It is a signal to the solvers that there are *multiple* "segments" at work here. You know, out of a total of say, 79 or something. Or was it 80? In any event, Clue Four and Clue Eight are from the same "segment." Clue One and Clue Seven are also from the same "segment," but not the same as Clue Four and Clue Eight. Clue Two is from another. Clue Three is from another. Clue Five is a play on words. And speaking of words, there was only one time I decided to use them.
A summary, and Lemli spoke only once, in "Turnabout Intruder."
10. Answers have been guarded. Surely there is more security to be found in virtual anonymity and near silence. I wear it all like a red badge of courage.
More clues pointing to a security guard and the near-silence, which I figured would eliminate Leslie and Galloway/Johnson.
Well, I enjoyed it anyway.

Nice guesses by everyone. I'll make my next one easier so I don't get a rep or something.

Henoch, you have the conn!