In a large bowl, whisk together the flour, sugar, baking powder, baking soda, salt, and poppy seeds.
In a separate bowl, whisk together the melted butter, vegetable oil, eggs, sour cream, vanilla extract, lemon zest, lemon juice, and milk until smooth.
Pour the wet ingredients into the dry ingredients and gently fold together using a rubber spatula. Avoid overmixing.
Cover the bowl with plastic wrap and allow the batter to rest at room temperature for 1 hour.
Meanwhile, prepare the lemon simple syrup by combining lemon juice and sugar in a saucepan over medium heat. Bring to a boil, then reduce to a simmer for about 5 minutes until the sugar dissolves completely.
Carefully peel the zest from one lemon and place it into a heatproof bowl.
Pour the hot syrup over the lemon peel and let it cool while the batter rests.
Preheat the oven to 425°F (220°C) and line a muffin pan with 11 paper liners.
Using a large scoop, fill each liner almost completely full without stirring the batter excessively. Resting helps create tall Lemon Poppy Seed Muffins, so handle the batter gently.
Bake for 8 minutes.
Without opening the oven for long, reduce the temperature to 350°F (175°C) and continue baking for 8–10 minutes until a toothpick comes out with only a few moist crumbs.
Immediately brush the warm muffins generously with the cooled lemon simple syrup.
Cool in the pan for 5 minutes before transferring to a wire rack. Sprinkle with additional poppy seeds if desired.