In a large mixing bowl, combine the butter, cream cheese, egg, lemon juice, and lemon zest.
Beat for one minute with an electric mixer on medium high. Make sure to scrape sides and bottom of bowl.
Add cake mix in two increments, beating well and scraping sides & bottom of bowl between additions.
Cover mixing bowl and refrigerate for 3 to 4 hours.
Preheat oven 350 degrees F.
Cover a cookie sheet with parchment paper.
Using a small scoop, drop the cookie dough on the cookie sheet.
Bake for 10 to 11 minutes. Cookies will not brown on the top, but the bottom should be light golden.
Place a cooling rack on a cookie sheet.
Put baked cookies on the cooling rack/cookie sheet.
To prepare glaze: mix together powdered sugar, milk, lemon juice, and lemon zest. Glaze should pour off a spoon, but should not be runny. Adjust with more powdered sugar, or more lemon juice, to get desired consistency.
Using a spoon, drizzle glaze over cooled cookies.
Store in an airtight container, with wax paper between layers of cookies.