Ironically, the most striking example of compassion the George offers to Lennie is taking his life at the end of the novel. Obviously, George's constant care for Lennie throughout the novel is one example of his compassion (even though Lennie has been run out of Weeds for assaulting a woman sexually).
George's killing of Lennie at the end of the novel has been foreshadowed by the killing of Candy's old dog earlier in the novel. Now, in the novel's final chapter, George does for/to Lennie what Candy himself could not bear to do for his old dog (Carlson shoots the dog with his Luger). George kills Lennie with the same weapon that Carlson used to shoot Candy's dog.
After George kills Lennie, Slim acknowledges that George had to take the action he did:
Slim said, “You hadda, George. I swear you hadda. Come on with me.”
He led George into the entrance of the trail and up toward the highway.
George keeping hope alive for Lennie - this runs throughout the book. George ending Lennie's life