After Candy shows George the dead body of Curley's wife, George tells Candy to wait a few minutes before telling the rest of the men on the ranch what has happened. During that time it is presumed that George snuck into the bunkhouse to get Carlson's Luger. He already had it on his mind that he would have to shoot Lennie. Steinbeck provides foreshadowing for this earlier in the book when Candy tells George that he should have shot his dog himself, instead of letting a stranger do it. Rather than let Curley or Carlson shoot Lennie, George must do it himself. After talking to Slim about what might happen to Lennie, George makes up his mind. When Carlson goes to look for his gun it is gone. George suggests that it may be lost but Carlson insists that Lennie has stolen it. In the last scene George lies to the men about Lennie having the gun:
But Carlson was standing over George. “How’d you do it?” he asked. “I just done it,” George said tiredly.
“Did he have my gun?”
“Yeah. He had your gun.”
“An’ you got it away from him and you took it an’ you killed him?”
“Yeah. Tha’s how.” George’s voice was almost a whisper.
Because it seems as though George killed Lennie in self defense he would be absolved of any wrong doing in the incident. In my opinion, this was not George's primary concern. The use of the Luger is symbolic because it was the same gun that shot the dog, Candy's best friend. George's act is one of compassion for his friend. That he might be guilty of murder is not George's concern. Making sure that his friend died humanely is his primary objective in his final act toward Lennie.
Although George agrees with Carlson when Carlson says that Lennie was the one who stole Carlson's gun, it was really George, and not Lennie, who stole it.
George lies about the gun because he does not want anyone to know that he came out with the intention of shooting Lennie. He wants to make it sound like he had no choice. Otherwise, he could be in trouble. First of all, he could possibly be charged with murder. Second, Curley's family might be mad at him because he deprived them of the chance to get revenge on Lennie.