Here we get a glimpse at the struggle that roils just beneath Lucy's exterior. Notice how she alternates between pleading and threatening? Speaking in terms of the development of her personality, the threatening would eventually win out. Later Lucy would probably pop the balloon just from the dire intensity of her incredible wrath.
The lead panels, not printed by some papers and thus optional, are interesting here. What do put put in those panels so that it's still understandable from their absence, but still in some way contributes to the story? Schulz had yet to hit upon his trick of putting an abstract drawing in the first panel. Here, they're used to underline the point that Lucy has anthropomorphized the balloon.
This is also the first strip I've noticed in which Peanut's catch-all expletive "Rats" is used.
