This strip makes no sense if you don't remember Lucy's prior fussiness over cutting sandwiches. This indicates that Schulz feels confident enough in her personality that he can use the character as a symbol of it, just like Schroeder is a symbol of both the artist and musicians in general.
This is different from Snoopy being a symbol of, say, dogs, or Linus of babies, because that's obvious from immediate reading.
The only other example of what I'm talking about that springs to mind are Charlie Brown's tantrums when faced with another character's quirks. Violet's mud pies don't count because Schulz only uses that in a context where the reader is reminded of her mud pies.
