Position racks in the upper and lower thirds if the oven and preheat to 350 degrees . Line 2 cookie sheets with parchment paper. Using a food processor, mix the oats until powdery, about 30 seconds. Blend in the flour, sugar, cornmeal and salt.
In a medium bowl, whisk together the butter, egg, lemon peel and vanilla. With the food processor on, add the butter mixture to the flour mixture and process the dough until the dough just comes together. Transfer the dough to a lightly floured surface and knead to blend. Halve the dough and form into 2 disks; wrap with plastic wrap and refrigerate for 15 minutes.
Transfer 1 dough disk to a lightly floured surface, then roll out 1/4 inch thick. Using a 2-inch cookie cutter, cut out 12 cookies and transfer to a prepared cookie sheet, rerolling the scraps to make more cookies. Repeat with the remaining dough. Bake the cookies, switching and rotating the pans halfway through, until lightly golden, about 12 minutes. Transfer to racks to cool.