(Answered by Max Gretinski)
John Lennon happened to be present (on September 29, 1967) when the first mono mixes of the song were being made. He decided at one point to switch on the radio, and to mix in a broadcast of whatever was playing at the time. It happened to be a radio performance of Shakespeare’s King Lear, with John Gielgud playing Lear.
When the radio switched on, the play was at Act IV, scene vi. Oswald eventually dies in that scene.
In the earlier portion, they mix the radio in only at the end of lines:
“I am the egg man.” (mix in radio)
“They are the egg men.” (mix in radio)
“I am the walrus. Goo goo goo joob.” (mix in radio)
The lines that got mixed in are the ones that appear highlighted here.
During the song’s fade, Lennon simply had them mix in the radio from a certain point on. We hear a fight, and then …
They fade the song out just after the line, “Sit you down, father; rest you” — which creates a rather appropriate ending.
Every Moment Has A Song 