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We've recently seen more hints about Lucy's developing self-centered personality. We've seen a little of it before in one prior strip, but this here is the true beginning of Lucy's long-running crush on Schroeder, what Charles Schulz had been known to call her "weakness."
While Lucy can be bossy, crabby and fussy, in some ways she's rather admirable. She has a very strong personality, is (usually) very confident, and doesn't often take 'no' for an answer. The second panel here is a good depiction of this side of her. Generally the Schroeder strips depict Lucy at her best, although this is far from universal.
Panel three is rather abrupt if the first two panels, which newspapers sometimes remove, are missing. The only previous hint of Lucy having a crush on Schroeder was that other strip almost a whole year back.
Most Lucy vs. Schroeder strips make the musician a bit more inscrutable. We're usually on Lucy's side in the struggle. That had yet to develop in this strip, which is more egalitarian in presenting clash of the characters' wants.
We get another somersault here.