Charles Schulz was thinking about the potential humor in lemonade stands for a long time. Like in this strip from October 18, 1950 (the first month of Peanuts) https://twitter.com/SchulzMuseum/status/1296447320977027073
And, of course, the idea goes back further than that! Here's a panel from Schulz's Li'l Folks from November 2, 1947 (three years before Peanuts!)
Schulz knew he was onto something when he needed an illustration for the back cover of You’re Out of Your Mind, Charlie Brown, the collection reprinting strips from 1956-'59. Maybe it was the title that made him think of it ...