Zest and juice the lemon(s) - you will need 2 tsp of juice for the cookies/ 2 tsp of juice for the glaze and 2 tbsp of zest for the cookies. One Lemon should be enough depending on the size of the lemons. If you want extra for decorating the tops of the cookies, you may need a second lemon.
In a small pot, melt the butter. The minute it starts slightly bubbling take the pot off the heat and add the lemon zest. Stir to combine and set aside to cool to room temperature.
In a small bowl add the flour, baking soda and cream of tartar: whisk to combine and set aside.
In a medium bowl add the room temperature melted butter with lemon zest, lemon juice, yogurt and sugar; whisk to fully incorporate, about a minute.
Add the dry ingredients to the wet ingredients, mixing until just combined.
Place the batter in the refrigerator, preheat the oven to 350F and prepare 2 cookie sheets by lining them with parchment paper. Once the oven is ready take the batter from the refrigerator and scoop dough balls with a 3 tablespoon scoop, roll the balls between your palms to smooth them out, roll them in sugar and place on a prepared cookie sheet. Bake the cookies for 12 minutes. Once out of the oven let the cookies rest on the pan for 5 to 10 minutes then transfer to a cooling rack.
While the cookies are cooling the glaze can be prepared. In a small bowl combine the powdered sugar and lemon juice, stirring until it is well combine and smooth. Once the cookies reach room temperature the glaze can be drizzled on. A little zest can be sprinkled on each glazed cookie for a final look if you choose.