I agree with kiwi - George does unfortunately underestimate Lennie's ability at times. Lennie does have the ability to remember the dream about the farm that he and George are going to have, and of course, the rabbits that he wants as pets. Lennie only wants George to re-tell it all the time because he loves hearing the dream become real through George's words. Note that Lennie pre-empts George when George re-tells the dream, telling George what to talk about next, which obviously indicates Lennie remembers the dream, perhaps even better than George does. Of course, what Lennie remembers at the end is to hide in the bush if there is any trouble, so that he is protected, at least initially, from the ranch hands as they look for him. This allows George to find him first and to do what he tragically needs to do.
Actually Lennie can remember more than we (or even George) initially give him credit for. He remembers the whole of the story about ‘the fatta the lan’’, he just likes to hear George tell it. He is also very clear on the animals they will have and the jobs he will do when the two men get their farm.
"I remember about the rabbits, George."
"The hell with the rabbits. That’s all you can ever remember is them rabbits."
He remembers that a ‘lady’ used to give him mice to play with, although he does not remember that she is his Aunt Clara.
Finally, he remembers George’s instruction to ‘hide in the brush’ when things go wrong on the ranch. Lennie heads for the brush straight after he kills Curley’s wife, and George knows to go there directly to reach Lennie before the lynch mob do.
Since Lennie really likes to pet soft things (par of the reason why he carried around a dead mouse for so long) he will always remember his dream to one day take care of rabbits on a farm with George. For Lennie this is the only thing he can grasp in world where nothing makes sense and everything constantly confuses him.