George Milton and Lennie Small are the dual protagonists of the John Steinbeck novel Of Mice and Men. Although close friends, they form something of an odd couple, in that George must serve as guide and protector for the mentally challenged Lennie, whose sizable frame contradicts his name.

As chapter 5 begins, Lennie has found a dead puppy in a barn and is stroking it—more to console himself than for any other reason. He worries that if George finds out about the puppy, he won't let him take care of the rabbits on the farm of their dreams. At first, he tries to hide the pup, but then he angrily hurls it across the room, believing that George will eventually find it anyway.

Curley's wife, an unhappy woman who George has warned Lennie to avoid, finds him in the barn, and begins to pour out her tale of woe. The bewildered Lennie, still petting the dead puppy, tells her that he likes to pet soft things. Hearing this, she invites him to stroke her hair. When he does, her hair becomes tangled, and she angily demands that he stop, but he continues, clutching her even more tightly. When she screams to be released, he covers her mouth, and unaware of his own tremendous strength, accidentally suffocates her to death.

While George and the others search for Lennie, he has fled to the Salinas River. He imagines first his Aunt Clara and then a giant rabbit scolding him for not listening to George, who he knows will be mad at him. He knows he has done something very wrong and now won't be allowed to tend the rabbits on their farm.

In Steinbeck's Of Mice and Men, Lennie also tries to cover the puppy up and hide it.  If he can keep George from finding out that he has killed the puppy, he won't get into trouble.  He is also somewhat comforted by Curley's wife, who tells him the pup is nothing and can easily be replaced.

In contrast, Lennie, after killing Curley's wife, very quickly sneaks out of the barn and, the reader learns later, goes to the spot George told him to go to if he gets in trouble. 

This does demonstrate that Lennie understands the difference between killing a puppy and killing a human being.

When Lennie kills the pup, he is upset at first because he thinks that George will not let him take care of the rabbits at their dream ranch.  Then he gets angry at the puppy for dying.

By contrast, Lennie is upset when he kills Curley's wife because he knows that he has done something bad.  He is not upset because of what George will think.  Instead, he is upset because he knows that he did wrong.

This shows to me that Lennie may be a bit slow, but he does realize that killing  a person is a huge deal.  So it tells me that he is not completely unaware of what is what in the world around him.