Given the circumstances, George makes a judicious decision in his mercy-killing of animal-like Lennie, who seems to act more on instincts than on reasoning. Nevertheless, there seems little, if any, justice in the conclusion of Steinbeck's novella. For, Lennie's act is accidental as he does not know how to control his strength; also, Curley's wife, albeit the Eve-like temptress and cruel, does not really deserve to lose her life because of her sensuous actions towards Lennie and her cruel words to Crooks.
The injustice of the ending of the lives of Lennie and Curley's wife point to the hopelessness and futility of the lives of the characters set amid the Great Depression, itself a time of great despair. Their dreams of owning a small ranch and of being an actress are, like the American Dream, but illusions.
In his essay, "Of Mice and Men: A Teachable Good Book," Thomas Scarseth suggests that Steinbeck's novella is a tragedy in the traditional sense of the demonstration of greatness during and in spite of defeat. For, Steinbeck shows that all men, lowly as well as high, are capable of "tragic nobility." Alluding to the book's title as well, Scarseth writes,
The best laid plans go oft astray because they come in conflict with one another. The simplest good intention— simply to stay alive—of a simple mouse, a simple pup, a simple young woman, is thwarted by Lennie's urge to pet something soft and beautiful. Lennie's drive to touch beauty kills the things he loves.
Truly, then, Lennie's death is tragic as he, in Steinbeck's own words, represents the "inarticulate and powerful yearning of all men" that is thrawted by an indifferent and heartless world as represented by the alienated "bindle stiffs."
Indeed, while the climax of the novel might be described as tragic and poignant, one might argue also that George's mercy killing of Lennie is a 'just' act.
One has only to consider the rough 'justice' which Curley wishes to dispense; in reality, a selfish determination to exact revenge for his crushed hand (and bruised ego) more than an act borne out of wild grief for the death of his trophy bride.
George understands that shooting Lennie himself is the lesser of two evils; prompted by Candy's regret that "I should have shot that dog myself, George. I shouldn't have let no stranger shoot my dog" but also realised through a discussion with Slim who implies that if they catch Lennie they could "lock him up and strap him down" before adding, "but that aint no good, George." Slim recognises that Lennie's life would be miserable - a form of punishment for an accident; one which Lennie would not even remember having been involved in.
And so, "woodenly", George carefully prepares himself to undertake the unthinkable. Note that George instructs Lennie to remove his hat, claiming that "the air feels fine." This is because George wants to ensure a quick, painless death and needs to ensure a clean shot. Furthermore, George insists that Lennie "look acrost the river" and instructs hime to imagine their dream ranch; this is to ensure that Lennie is not cognizant of his fate or frightened by the Luger pistol and instead, Lennie is thinking of a future which George knows does not exist for him. Lastly, we read that "Lennie giggled with happiness" and, in this way, we are comforted by the fact that Lennie dies at his happiest - thinking of feeding alfalfa to the rabbits.
This is in marked contrast to the agonisingly slow death which Curley wanted Lennie to suffer; remember, Curley instructed the men to shoot for "his guts" - wanting Lennie to suffer and experience the kind of pain Curley himself endured when Lennie crushed the bones of his hand the night before.
So, is it 'just' for George to end Lennie's life? One might argue that Lennie's swift, painless death is infinitely preferable to the prolonged suffering Curley wishes to inflict - for all the wrong reasons!
Hope this helps!