Preheat the oven to 400 degrees F (200 degrees C). Grease a rectangular baking dish with butter.

Cream 1 cup plus 2 tablespoons butter and sugar in a bowl with an electric mixer until smooth. Add eggs one at a time, beating well after each addition. Combine flour and baking powder in a separate bowl and mix into the batter 1/4 cup at a time. Beat in lemon zest. Pour batter into the prepared baking dish.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 40 to 45 minutes. Cool on a wire rack for 5 minutes. Run a table knife around the edges to loosen. Invert carefully onto a serving plate or cooling rack. Let cool completely, 30 minutes to 1 hour.

Combine cream cheese and butter in a bowl and beat with an electric mixer until creamy. Add confectioner's sugar 1/4 cup at a time, alternating with lemon juice, mixing until frosting has the desired consistency.

Poke holes 2 to 3 inches apart into 1 side of a styrofoam block using a lollipop stick.

Trim off tops and sides of the cake. Crumble the cake into very fine crumbs using your hands. Mix in 2 tablespoons frosting until thoroughly combined. Add more frosting if necessary until mixture is smooth and sticks together.

Line a baking sheet with waxed paper. Roll the cake mixture into walnut-sized balls. Arrange cake balls on lined baking sheet and refrigerate for 30 minutes.

Melt 1/4 of the confectioners' coating in a microwave-safe glass or ceramic bowl in 15-second intervals, stirring after each melting, 1 to 3 minutes.

Poke a small hole into each cake ball with a lollipop stick. Dip lollipop sticks into the confectioners' coating and stick one into each cake ball. Refrigerate for 30 minutes.

Melt remaining confectioners' coating in a microwave-safe glass or ceramic bowl in 15-second intervals, stirring after each melting, 1 to 3 minutes. Dip cake balls into the coating; tap to remove excess coating. Scatter sprinkles over the cake balls. Stick cake pops upright in the prepared foam block. Allow to dry completely.