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The episode trivia on the DVD menu mentions that Lon Chaney Jr.'s "role of Lenny in this episode is a lampoon of his role of Lennie Small in the film Of Mice and Men."
I think there's a bit more to it than that. I haven't seen the 1939 movie, but I have read Steinbeck's book (albeit only once and about two and a half years ago; some of the delay in writing this was my looking up some things). Like the two bandits in the Monkees episode, the two main characters in Of Mice and Men are named George and Lennie.
In one scene in the episode, the Monkees pretend that they want to play baseball (using a shovel as a bat), but really they just want to acquire the shovel so they can try to dig their way out of a jail cell. After they have the shovel, Micky asks Lennie, "Hey, can we use your ball?" Lennie puts his hands in his pockets, and he brings them out with the ball and a dead mouse:
Early in Of Mice and Men (it's page 7 in the Penguin Classics edition, which is what I have), Steinbeck's Lennie also has a dead mouse in his pocket. He tells George he has it there so that he can "pet it with my thumb while we walked along."