Preheat oven to 375 degrees. Place granulated sugar in shallow bowl.
Beat 3/4 cup butter in large bowl with electric mixer to medium speed until fluffy. Add egg and lemon peel; beat 30 seconds.
Add cake mix, 1/3 at a time, beating at low speed after each addition until combined. Stir in cornmeal. (Dough will be stiff).
Shape dough into 1-inch balls; roll in sugar to coat. Place 2 inches apart on ungreased cookie sheets.
Bake 8 to 9 minutes or until bottoms begin to brown. Let cookies stand on cookie sheets 1 minute; transfer to wire racks to cool completely.
Meanwhile, beat powdered sugar and remaining 2 tablespoons butter in small bowl with electric mixer at low speed until blended. Gradually add enough lemon juice to reach spreading consistency.
Spread 1 slightly rounded teaspoon frosting on bottom of one cookie. Top with second cookie, bottom side down. Repeat with remaining cookies and frosting. Store at room temperature for up to 24 hours or freeze.