Preheat oven to 400 degrees F (200 degrees C). Grease 12 muffin cups, or line with paper muffin liners.
Mix flour, 3/4 cup sugar, baking powder, baking soda, and salt in a large bowl; make a well in the center of the flour mixture. Mix zucchini, yogurt, butter, egg, 1 tablespoon lemon juice, and 1 tablespoon lemon zest in a separate bowl; pour yogurt mixture into well. Gently stir yogurt, slowly incorporating the flour mixture until just blended. Batter may be slightly lumpy. Pour batter evenly into prepared muffin cups.
Bake in preheated oven until a toothpick inserted into the center of a cupcake comes out clean, about 20 minutes.
While muffins are baking, whisk 1/3 cup lemon juice, 1/4 cup sugar, and 2 teaspoons lemon zest together in a saucepan over medium heat until mixture comes to a simmer and sugar is dissolved, about 5 minutes. Cover and keep glaze warm over low heat.
Poke each muffin several times with a toothpick; spoon glaze over muffins. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.