Preheat oven to 325°F.
Cream together goat cheese, butter and sugar until light and fluffy. Beat in the eggs, one at a time, until incorporated. Mix in the lemon juice and zest. Mix in the flour. Use a 1 Tbsp scoop and drop rounded balls of dough onto cookie sheet. Bake for 7-8 minutes until set — cookies should not brown and will not spread very much. Allow to cool before frosting.
For the frosting, beat together the goat cheese and lemon juice until smooth. Add powdered sugar ½ cup at a time, mixing until incorporated. Add enough powdered sugar to form a very thick glaze. Pipe frosting on to cooled cookies and add a bit of zest to each.