The first review I read of this episode really hit the nail on the head, but I'll write my own anyway. Maybe I have too much time on my hands?
This episode begins with our gal going over her finances. Let's just say she isn't happy with the results. But someone else is even less happy. Want to take a guess who that might be? No, not Fred. It's Ricky, of course. Can't believe you couldn't figure that one out genius. Anyway, the bottom line is that Lucy needs money. And we all know she can't make it by singing. Fortunately (and all-too coincidentally) for her, Ethel is able to get her a spot on a radio show where the grand prize is $1000. That's not a bad figure, even today, especially for the work involved. Lucy is told she must introduce a man to Ricky as her long-lost husband and keep him believing it until 12:00. Sounds easy, but things go horribly wrong when a bum shows up at the door and Lucy mistakes him for the man from the radio show. As the other review pointed out, there are a lot of holes in this story. No radio show in the world would rely so much on physical humor or a stunt that takes place entirely outside of the studio. They might as well have just given her the thousand dollars! Of course, it can mostly be forgiven since much of what follows is funny. This episode is also notable because it marks the first appearence of Frank Nelson on the program. Nelson would appear in many more episodes. He's also the inspiration behind the Simpson's character who always says, "yeeeeessssss?"
Anyway, this is a pretty typical early episode of Lucy. My personal feeling is that the show didn't really hit it's stride until the latter half of the first season. That's true of many shows though, and by that measure, Lucy's early episodes are still pretty impressive.