With an electric mixer, cream butter and sugar, until fluffy. Add lemon zest, ricotta and vanilla extract. Beat well.
Beat in eggs one at a time, and mix until well blended. Scrape the sides of the bowl. Add the flour, baking soda, and salt, mix until combined. Cover dough and chill for at least 2 hours or up to 2 days.
Preheat oven to 350 degrees. Line a baking sheet with parchment paper or silicone baking mat. Drop by rounded tablespoons on baking sheet. Bake cookies for 12-14 minutes or until the bottom of the cookies is golden brown. Transfer cookies to cooling rack.
In a mixing bowl, mix together powdered sugar, milk, vanilla, and fresh lemon juice. Adding more milk as necessary to make a smooth icing. Dip cooled cookies in icing. Allow icing to set before storing in an airtight container.