You can find many quotes in Of Mice and Men that reveal Lennie's childlike nature. For instance, when Steinbeck allows us to listen to Lennie's thoughts, we realize they are simple and often revolve around not wanting to disappoint George or incite his anger. He treats George not as a friend but as a parent figure whose guidance he relies on. Like a child would with a parent, Lennie also often turns to George for comfort, asking him to repeat again and again the story of the farm they will buy so they can live off the fat of the land.
Lennie shows his childlike nature in his love of animals and his desire to touch and stroke pretty things, be it the fur of a puppy or Curley's wife's hair. Like a child, he can fail to have good judgment about not hurting smaller creatures, often not realizing his own strength. He also uses simple words, just as a child would, because he lacks a sophisticated vocabulary.
A quote that shows Lennie's childlikeness is as follows. In it, Lennie, who has just accidentally killed Curley's wife, confesses to George as if he were his parent, using the simplistic words "bad thing" to describe his behavior:
Lennie said, “George.”
“I done another bad thing.”
This is not the complex language of an adult, who would probably rationalize his behavior, express extreme guilt, or try to blame someone else. Lennie, in contrast, can't seem to quite understand what he has done beyond that it is "bad."