George killed Lenny with a gun he stole from Carlson. They were by the river where the exposition to the story takes place and George was telling Lenny about the farm they were going to have when he shot him in the back of the skull.
George kills Lennie out of love. Lennie accidentally killed Curley's wife, George knowing that there was no way he could save Lennie from the crime. Instead of Curley or someone else killing Lennie, George does so.
