Preheat the oven to 350 degrees F.
Cream the butter and the sugar together. Add the eggs one at a time and mix in.
Mix in the lemon juice and zest.
Sift together the flour, poppy seeds, baking soda, cream tartar, and salt. Add to the wet ingredients and mix in.
Once the cookie dough is completed, roll dough into about 1 inch balls. Place on an ungreased cookie sheet. Bake for 10 to 12 minutes or until the bottom of the cookies are starting to brown.
Remove from the oven. Then remove from the cookie sheet and cool completely on a cooling rack.
While the cookies are baking mix together the lemon icing. In a small bowl add the powdered sugar and gradually add the lemon juice until you have the right consistency for icing the cookies.
Once the cookies are completely cooled spread each cookie with the lemon icing.