I think we can safely assume that the upper graffiti is Patty's doing. It is important to the joke here that Lucy is depicted as very young, so as to provide an explanation for the illegible scrawl on the bottom of the fence. In fact, I think Schulz is actually cheating Lucy slightly shorter than she usually is, so the joke is clearer.
The strip for February 12, 1954 (presented here, fourth down) has Shermy writing on a similar wall. On that strip, njguy54 commented that Shermy's use of cursive was "interesting." It was, there, since who writes in cursive on large, vertical surfaces? But the use of cursive here is much more important, since it provides important visual similarity between the two writings.
Did Schulz plan the two strips at the same time? Probably; there are many examples of similar strips separated by a small number of days, enough to suggest part of his creation strategy: to hit upon some idea, to mine it for joke potential, then to draw some or all of the ideas, ideally seperated by a few days to keep things mixed up.
At some point, I conjecture, Schulz realizes that he doesn't always have to spread the strips apart like this, and he takes to running "theme weeks," where a number of consecutive strips feature a similar premise. That eventually leads to sequences of linear storytelling, such as Charlie Brown progressively leading his baseball team to failure. (Another sequence leading to that is the upcoming Lucy in the Golf Tournament story that plays over consecutive Sundays.)
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