Place the sugars and butter in a large bowl and beat well with an electric mixer until blended, about 1 minute. Add the egg, milk, vanilla, and lemon zest until combined. Scrape down the sides of the bowl. Beat in the oats. Turn off the mixer.
Stir the flour, salt, and baking soda together and add gradually to the batter, on low speed. Scrape down the sides of the bowl.
Place a 16-inch piece of waxed paper on the counter, and drop spoonfuls of the dough lengthwise on the paper, making a line about 12-inches long. Fold the paper lengthwise over the dough to make a log, rolling to 1 ½- to 2- inches in diameter. Place the log of dough in the fridge to chill for 12 to 24 hours.
When ready to bake, preheat the oven to 400 degrees F.
Remove the dough from the fridge, and place on a cutting board. Remove the waxed paper. Cut the dough into ¼-inch slices and place these on the baking sheet about 2 inches apart. Place the pan in the oven.
Bake the cookies until they are golden brown around the edges, about 8 to 10 minutes. Let the cookies cool on the pan 1 to 2 minutes, then remove to a wire rack to cool completely. Repeat with the remaining dough.