In a large bowl, combine the granulated sugar and lemon zest. Use your hands to rub the zest into the sugar for about 30 seconds to release its oils and boost the lemon flavor.
Add the melted butter, oil, eggs, milk, sour cream, and lemon juice. Whisk until well combined.
In a separate large bowl, whisk together the flour, baking powder, baking soda, salt, and poppy seeds.
Pour the wet ingredients into the dry ingredients and gently fold the batter together with a spatula—do not overmix. Cover and let the batter rest at room temperature for 1 hour. (This will ensure tall muffin tops.)
After 45 minutes, preheat the oven to 425°F. Line a 12-cup muffin pan with paper liners or spray with nonstick cooking spray.
Once the batter has rested, gently scoop it into the muffin cups, filling them to the top. Avoid overworking the batter.
Bake on the center rack at 425°F for 6–7 minutes, then reduce the temperature to 350°F and bake for another 7–8 minutes. Do not open the oven while baking. Check for doneness with a toothpick—it should come out clean or with a few moist crumbs.
Let the muffins cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.
While the muffins cool, you can prepare the glaze. Whisk all glaze ingredients in a small bowl until smooth and pourable. Adjust consistency with more powdered sugar or lemon juice as needed. Drizzle over cooled muffins.