The episode in question was first broadcast in 1936 during Oboler's first year as writer/producer of Lights Out; then, it was dubbed "Across the Gap." We don't seem to have a surviving copy of this broadcast, but the 1942 version (usually called "Neanderthal") is with us and can be downloaded from archive.org here.
In this play, a Frenchman, American man and British lady are traveling together via motor car. The Frenchman believes in solving problems with his bare hands, holding a very pragmatic outlook; the American is a diplomat who thinks reason will solve mankind's problems; the British lady doesn't seem to hold any opinions - we might (charitably) consider her as being undecided.
Being an Oboler play where people who openly voice their philosophies must then face them in grim, stark reality, they crash their car and travel back in time (just roll with it). They encounter a Neanderthal man and the American attempts to reason with it, but eventually must concede that for the sake of survival, he must kill the Neanderthal.
In 1936, Oboler meant the play to comment upon the situation in Europe, the rise of fascism and looming threat of Nazi Germany. Strangely though, the allegory he created doesn't quite fit. Prior to World War II, the British were the ones who thought reason & diplomacy could solve the problem while the Americans were neutral. Surely the perfect allegory would have been a British diplomat accompanied by a weak-willed American woman (Oboler's stereotype, not mine)? Surely by 1942 it would have been obvious to Oboler that the British in his story were a little miscast.
Truly, the British lady is a distraction - Oboler surely meant the diplomacy-speaking American to represent his isolationist brethren who had to learn an important lesson about standing up against aggressors; that part of the allegory works and - fortunately for Oboler - history has justified his position.
Er, that's it - that's what I thought. Thanks for indulging me.