Heat oven to 350°F; line sheets with parchment.
Cream butter and ½ cup powdered sugar in large bowl about 3 minutes until light and fluffy.
Mix in zest and 2 tablespoons lemon juice thoroughly.
Mix in flour and salt on low just until dough forms; do not overmix.
Roll into 1-inch balls; place 2 inches apart on sheets and slightly flatten with glass bottom.
Bake 10-12 minutes until edges start turning golden. Cool on sheet 5 minutes; transfer to rack.
Meanwhile, whisk 1½ cups powdered sugar and 3 tablespoons lemon juice smooth.
Drizzle over cooled cookies; set 30 minutes before serving or packing.