Since there are various editions of John Steinbeck's Of Mice and Men, it is often difficult to convey the correct page number. But, near the middle of the third scene in which George and Lennie talk privately, having forgotten old Candy who lies on his bunk morosely after Carlson has shot his dog, Lennie asks George to describe the farm that we will someday have. Overhearing them, Candy, turning slowly over, is drawn into their dream. As George invites Candy into their plan of a place of their own, he advises Candy not to tell anyone else as they may get fired. Lennie and Candy nod in agreement and "they were grinning with delight."
Then, in Scene 4, Lennie, who wants to pet the puppies, appears in the doorway of the barn. As Crooks scowls at Lennie, "Lennie smiled helplessly in an attempt to make friends." When Crooks tells him he has no right to enter, Lennie excuses himself, saying he has not done anything; then he tells Crooks that he has seen his light: "...I thought I could jus' come in an' set." In this scene, Lennie probably approaches kindness as much as he can in his child-like mentality that is really not capable of much altruism.
Some of your best options occur in chapter 1. I find much of the rest of the novel demonstrates Lennie's efforts to fend for his own needs. In fact, even in chapter 1, his acts demonstrate his own desires.
Lennie tells George:
"I wouldn't eat none, George. I'd leave it all for you. You could cover your beans with it and I wouldn't touch none of it... George, you want I should go away and leave you alone? ... I could go off in the hills there."
In my book this is on page 11. You have several instances of Lennie's effort to be selflessly kind to George. Lennie realized he had been demanding about beans and ketchup. He tried to demonstrate that if they even had some, Lennie would be willing to give it all to George because he valued George that much. Lennie even realizes the burden he is to George and offers to leave him alone.