It's worth reading this testimony by James Jarman. It establishes that, like most of the others, he went and got his lunch and ate it as soon as the lunch break began. He went and got a soda first on the second floor, and then he went and got his sandwich from the shelf in the domino room where he put it, and then he went and ate it. He didn't eat it in the domino room. He ate it over by the window looking out the building, but it was probably when he went in to get it that Oswald saw him.
Note: He did not confirm seeing Oswald. At least, it's not recorded that he confirmed it. I was told by Professor Gerald McKnight that in his first statement to Dallas Police he did admit to seeing Oswald at that time. But, even if we accept his statement to the Warren Commission at face value, it doesn't matter because Oswald saw him, and he was there. And that proves that Oswald was there, right around Noon or shortly thereafter, in the domino room eating his lunch.
Mr. BALL - What time did you quit for lunch?
Mr. JARMAN - It was right about 5 minutes to 12.
Mr. BALL - What did you do when you quit for lunch?
Mr. JARMAN - Went in the rest room and washed up.
Mr. BALL. Then what did you
Mr. JARMAN - Went and got my sandwich and went up in the lounge and got me a soda pop.
Mr. BALL - Where is the lounge?
Mr. JARMAN - On the second floor.
Mr. BALL - On the second floor?
Mr. JARMAN - Yes.
Mr. BALL. Then where did you go after you got your soda pop?
Mr. JARMAN - Came back and went down to the window.
Mr. BALL - What window?
Mr. JARMAN - Where Oswald and I was talking.
Mr. BALL - Where?
Mr. JARMAN - Between those two rows of bins.
Mr. BALL - Where Oswald and you had been talking?
Mr. BALL - What did you do there?
Mr. JARMAN - I was eating part of my sandwich there, and then I came back out and as I was walking across the floor I ate the rest of it going toward the domino room.
Mr. BILL. You say you ate the rest of it when?
Mr. JARMAN - Walking around on the first floor there.
Mr. BALL - Did you sit down at the window when you ate part of. your sandwich?
Mr. JARMAN - No; I was standing.
Mr. BALL - And did you have the pop in your hand, too?
Mr. JARMAN - Yes; I had a sandwich in one hand and pep in the other.
Mr. BALL - You say you wandered around, you mean on the first floor?
Mr. JARMAN - On the first floor.
Mr. BALL - Were you with anybody when you were at the window? Did you talk to anybody?
Mr. JARMAN - No; I did not.
Mr. BALL - Were you with anybody when you were walking around finishing your sandwich?
Mr. JARMAN - No; I wasn't, I was trying to get through so I could get out on the street.
Mr. BALL - Did you see Lee Oswald?
Mr. JARMAN - No; I didn't.
Mr. BALL - After his arrest, he stated to a police officer that he had had lunch with you. Did you have lunch with him?
Mr. JARMAN - No, sir; I didn't.
Mr. BALL - When you finished your sandwich and your bottle of pop, what did you do?
Mr. JARMAN - I throwed the paper that I had the sandwich in in the box over close to the telephone and I took the pop bottle and put it in the case over by the Dr. Pepper machine.
Mr. BALL - And then what did you do?
Mr. JARMAN - Then I went out in front of the building.
Mr. BALL - With who?
Mr. JARMAN - Harold Norman, Bonnie Ray, and Danny Arce and myself.