1. Bake cake according to box directions and cool completely. Break into chunks. Pulse in food processor into fine crumbs, working in batches. Transfer to a large bowl.
2. Add 1/2 cup frosting to bowl with crumbs. Mix with your hands until crumbs are moistened and can be molded like clay, adding additional frosting, 1 Tbsp. at a time, if necessary. Shape mixture into 1 1/4- to 1 1/2-inch football shapes; place on a parchment-lined baking sheet. Cover with plastic wrap and chill for at least 1 hour and up to 1 day.
3. Place a large piece of Styrofoam on a baking sheet. Mix chocolate chips and oil in top of a double boiler over simmering water. Cook, stirring often, until chocolate is smooth. Let cool to warm room temperature. Dip top of craft stick or lollipop stick into chocolate and insert partway into one of the footballs. Dip football into chocolate, letting excess drip back into bowl. Insert end of stick into Styrofoam to allow chocolate to harden while pops are upright. Repeat with remaining footballs. Refrigerate pops for 15 minutes to set chocolate.
4. Place white chocolate chips in a microwave-safe bowl and microwave on 50 percent power until just melted. Whisk until smooth. Transfer white chocolate to a pastry bag fitted with a small plain tip and pipe laces on each football pop. Chill until set, about 5 minutes.