The beginning of this strip demonstrates how Patty and Violet are slowly becoming a double-act, reinforcing each other's opinions and building up the will to confront Lucy. Lucy is also true to form here, fussing and throwing a tantrum about "not playing her way." (That generic reason for the confrontation and tantrum seems kind of weak, but it serves to keep the focus on the characters and their reactions, and not whatever game it is they're playing.)
This strip also demonstrates that Lucy's behavior is, to some extent, an act she puts on to attempt to get her way. When it's evident that her ruckus is to no avail she comes around quickly.
The drawings of her tantrum are very energetic. Panels five through ten show particularly varied reactions. Schulz must have put some thought into how to illustrate characters pitching fits or otherwise expressing anger/dismay. Note, Charlie Brown hit his own head against a tree not long ago, and now Lucy is doing it too.
