Well, I was partway right; she's washing every dish in the house and Lizzie wants a favorite food.
Panel 1: We start off with Elly washing dishes. As she does so, Lizzie says "Nizzie wan'cookie" Elly, who thinks that this means that Lizzie wants her to bake cookies, says "Not how, honey! Let's have some banana." Lizzie yells the terrible, awful word "No!!"
Panel 2: Having been browbeaten by Annie into thinking that she cannot simply buy cookies at the store, Elly makes do with a healthy substitute. As she cuts the banana into cookie-like discs, she tells Lizzie she's doing so; Lizzie's response is to gurgle 'Gah' in confusion.
Panel 3: She then says "Now we have a flower! Let's put sprinkles on the flower; pink on the outside, brown in the middle." Lizzie makes an enthusiastic "Yah" sound.
Panel 4: As Lizzie shrieks in delight, Elly says "Look! Pretty Flower! Lizzie EAT Pretty Flower!!"
Panel 5: Her happiness at being able to have steered her child away from junk food collapses when Lizzie declares that she still wants a cookie,
Summary: Lizzie's still wanting a cookie isn't very surprising to anyone who isn't Lynn. She never quite got it through her head that children that age aren't going to be deflected from wanting COOKIE NOW by pretty flowers, no matter how much Martha says they'll love them.