If L-1 did not want a beer, then he could answer the question “No.” That he didn’t say “No” means that he does want a beer. But he can’t answer “Yes” because he does not know about L-2 & L-3.
Similar for L-2.
But L-3 knows that L-1 and L-2 want beers, because they didn’t say “No.” So he can answer “Yes.”
Aaaaah.