Usually turnabout/chase strips only concern two characters, but Patty in this one is just a bystander.
So, let's return to the subject of the implications when one character chases another. Why does a character do so? It usually happens when the chased insults the chaser, or uses an exceptionally bad joke, usually appears angry while chasing, and it is implied that the chaser seeks violence. (Otherwise, what would that character do if he catches the other? Make him or her see reason through argument?)
Because of this, when a girl chases a boy it is funnier than when a boy chases a girl. We have reason to believe that Schulz saw it this way too; he has been recorded as saying a girl punching a boy is funny, but a boy punching a girl is disturbing.
The implications here are slightly allayed due to Lucy's spirited "WHEEE" in the last panel. At the very least she doesn't seem to feel threatened.
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