This is one of the few LITB episodes that center on Lumpy Rutherford; the only others that come to mind are "Lumpy's Scholarship" and a couple of early episodes in which Lumpy was a bully.
Angry with his dad, Lumpy has decided to quit school and join the Merchant Marines. Only thing is, he has had letters and pamphlets from the Marines forwarded to Wally's address so that his dad won't suspect anything. Now, when June discovers these communiqués she is sure that a recent reprimand from Ward has driven Wally to leave home.
Of all the regular LITB characters, Lumpy has always been the most difficult for me to like, but this episode succeeds in humanizing him - or at least making us feel pity for him. The relationship he enjoys with his father Fred Rutherford is dysfunctional, to put it mildly. Blowhard Fred likes to pretend he is the perfect up-to-date progressive father, full of the latest pop psychology. The reality is quite different, as we learn here: in this family the father doesn't know what the son is up to. You might say that Lumpy and Fred live in a mutually-fed world of delusion.
The character of Lumpy was memorably fleshed out (as it were) by the late Frank Bank. He played the role as a classic "follower" with little mind of his own, an oafish "second banana" to Eddie Haskell, with always just a touch of effeminate dopeyness ("Yes, Daddy!") that took away any menacing edge the character might have had.
On another note, I continually wonder why people call LITB a "simplistic" show. Nothing could be further from the truth. This episode has enough irony and emotional complexity for a one-act stage play, with camera work and acting that express the relationships among the characters. It's the small details that made this series great. Just one example: in the closing scene, Ward June and Beaver stand framed in the doorway watching Lumpy and Fred depart; but instead of a symmetrical arrangement, Beaver stands in front of Ward, almost obscuring him: the perfect visual metaphor of a son growing into manhood and taking the place of his father. Indeed, this is a prominent theme of the episode: at one point when Wally is scolding Lumpy for his behavior, Lumpy tells Wally that he sounds just like his father.
Just one example how artful a series LITB was.