Final answer:
Lucy asked Schroeder to play 'Jingle Bells,' a fact she only recognized when Schroeder simplified the tune to a single-finger performance, a humorous moment from the Peanuts series.
Step-by-step explanation:
The song that Lucy asked Schroeder to play that she didn't recognize until he finally played it with only one finger is "Jingle Bells." This comedic interaction is a classic moment from the Peanuts comic strip series, created by Charles M. Schulz, where Lucy, often seen leaning on the piano, requests tunes from the musically gifted Schroeder. The humor derives from Lucy's inability to name the tune properly and Schroeder's simplification of the song to its most basic notes, triggering her realization.