I am 28 years old. I work in retail. I know that a customer can return items even though they were on sale. So, why is it mentioned several times during the series that Lucy couldn't return items because they were on sale? Was it a legit rule for retailers back in the 1950s?

I think it was just written in the show that way to fit the plot...of course this is JMO.

I used to wonder about that, too. While I have seen stores put up signs that say "No refunds on sale items" or 'No returns or exchanges on sale items," in ILL it just seems to be automatically assumed that NO store will refund any merchandise that was 'on sale.' The idea seems to be accepted as competent, though. When Lucy buys the new couch and coffee table and tries at first to hide them from Ricky, then he confronts her and tells her she will have to return them, her response is that she bought them "on sale." And Ricky knows they can't be returned, then. But perhaps furniture is different from clothing or smaller items?-- if returned, there would be 2 deliveries and no gross profit for the seller.

Maybe back then a lot of stores wouldn't take sale stuff back.

In the Sears store I work in, we are told that a customer doesn't like furniture, they can return it. Of course, the fact that my store have packaged versions of furniture in stock doesn't hurt. Plus, even I order a piece of furniture online (via Sears.com) that my store doesn't carry, the customer is told that they CAN return it even if my Sears store doesn't carry it.