Yes, George's mercy killing of Lennie neatly parallels the events of Chapter Three, when Candy allowed Carlson to shoot his malodorous old dog. Steinbeck is even careful to involve the same Luger in each killing. Whereas the meek and passive Candy proved unable to do the job himself, George shows no such weakness. As has been proven beyond a reasonable doubt at this point, Lennie's lethal innocence is not compatible with the world. He cannot learn to change his ways - he cannot even understand why the "bad things" he has done are bad. The fate he would meet at Curley's (mutilated) hands - likely a drawn-out, vengeful lynching - is enough to convince George that his only real option is to make Lennie's death as quick and painless as possible.
It depends on the perspective. I think he did do the right thing to shooting lennie before the mod could have killed him. He knew lennie was suffering, and he wanted to put him out of his misery. This can be connected to the shooting of the old dog. The dog was in pain, and could have died a painful death, similar to lennie with the mob. It’s brings up the question of would you rather have a painless quick death, or a prolonged, painful death. If you pic the first one, then it was the right thing for george to do. This kind of prompts are solely based on opinions and using past references and foreshadowing to answer this question. look back at the book and especially near the the old dog event, why lennie got a mob after him, and the relationship between george and lennie.
