I found this cookie on the inside of a Land O Lakes butter carton. It's one of my favorites. Try it with your icing.

SLICE & BAKE LEMON CRISPS (6 1/2 dozen)
3/4 cup Land o Lakes unsalted butter, softened
1 cup sugar
1 egg
1 TBL grated lemon peel
1 1/2 cups flour
Sugar or powdered sugar
Combine butter & sugar in large mixer bowl. Beat at medium speed, scraping bowl often until creamy (1-2 minutes.) Add egg & lemon peel; continue beating until well mixed (1-2 minutes.) Reduce speed to low; add flour. Beat until soft dough forms (2-3 minutes.)
Divide dough in 1/2. Shape each 1/2 into 8" log (1 1/2" diameter) on lightly floured surface. Wrap tightly in plastic food wrap. Refrigerate until firm, 2 hours or overnight.
Heat oven to 350°. Cut rolls into 1/8-1/4" slices with sharp knife. Place 1" apart onto ungreased cookie sheets. Bake 8-12 minutes or until edges are very lightly browned. Let stand 1 minute; remove from cookie sheet. Roll cookies in sugar while still warm & again when cool. Variation: Stir 1/3 cup finely chopped almonds into dough after mixing in flour.~~

I love these cookies and they would be great iced like you said:

Touch of Lemon Sugar Cookies

{{!gwi}}

2 cups sugar
1 cup butter softened or Crisco
Zest of one lemon
1/4 cup fresh lemon juice
2 eggs
3 1/4 cup all-purpose flour
1 teaspoon salt
1 teaspoon baking soda
1 teaspoon cream of tarter
sugar to roll dough in

In large bowl, combine sugar, butter, lemon zest, lemon juice, and eggs. Blend until smooth. Stir in combined remaining ingredients; blend well. Chill 1 hour. Heat oven to 325°. Grease cookie sheets. Shape dough into 1-inch balls; roll in sugar and place on greased cookie sheets. Bake 13 to 15 minutes or until lightly golden edges. (Cookies will be soft in center.) Cool slightly, remove from cookie sheet.

Marilyn

Was the cookie itself lemony, or just the icing? And, was the cookie thick or thin?

Thanks so much for the recipes. I'll try both to see which one is closer. They both sound yummy. Westelle, the cookie itself wasn't very lemony as I remember. The icing was what melted in your mouth. It was a thicker cookie, not thin like a crisp, but larger with substance to it. The restaurant baked and sold differnt kinds of cookies along with gourmet sandwiches and salads. With each meal, you got your choice of cookie for dessert.