Lunch Challenge

Okay, so Kate is a GREAT breakfast eater.
For Breakfast she eats: A healthy cereal (such as wheat Chex, Raisin Bran, or Cheerios with sliced bananas), some yogurt, 8 oz. 2% milk, and sometimes a little whole wheat toast.
I couldn't feel better about it or more proud of what she's eating.

Then for a snack: she will have: some crackers, some of a banana, or string cheese. Of corse she's drinking water from her sipping throughout the day too.

Her nap is before she's hungry for lunch...

PROBLEM:
So after she wakes up from her nap (around 3:00pm) I try to think of something she'll want to eat.

I offer her: a peanut butter and honey/or jelly sandwhich, more yogurt, and her water. She usually doesn't want her sandwhich (or not very much of it). She's totally disinterested and would rather play.

WHAT SHOULD I DO? Any suggestions based on everything I've said?