Whisk the flour, sugar, baking powder, baking soda, salt, and poppy seeds in a large bowl. Combine the melted butter, oil, eggs, sour cream, vanilla, lemon zest, lemon juice, and milk in a separate bowl until smooth. The wet mixture should look creamy and evenly blended, with flecks of lemon zest throughout.
Add the wet mixture to the flour mixture and fold with a rubber spatula only until no dry flour remains. Cover the bowl with plastic wrap and leave the batter at room temperature for 1 hour. The rested batter should become thick, airy, and capable of holding a soft mound.
Place the fresh lemon juice and sugar in a saucepan over medium heat and bring the mixture to a boil. Reduce to a simmer and cook for 5 minutes so the sugar fully dissolves. The syrup should look clear and gently bubble rather than appear grainy.
Remove the peel from 1 lemon and place it in a heat-safe bowl. Keep the peel ready while the syrup finishes cooking. Use peel with minimal white pith so the syrup stays bright rather than bitter.
Pour the hot syrup over the lemon peel and let it cool at room temperature while the batter rests. The peel will release a fresh citrus fragrance into the syrup. The syrup should smell sweet and lemony as it cools.
Near the end of the resting time, heat the oven to 425°F and line a muffin tin with 11 paper liners. Arrange the pan on a centered oven rack. Starting with a fully heated oven gives the muffin tops their strongest initial lift.
Use a large 2 oz scoop, or about 1/4 cup, to fill each liner to the top and slightly above it. Handle the batter gently while portioning so it stays light. Each liner should hold a rounded mound of thick batter.
Bake for 8 minutes at 425°F, then lower the oven setting to 350°F and continue baking for 8 to 10 minutes. Check with a toothpick near the center of a muffin. The toothpick should come out with a few moist crumbs, and the tops should spring back lightly under a clean fingertip.
Brush the hot muffins generously with the lemon syrup as soon as they come out of the oven. Let the syrup absorb into the warm tops. The surface should look lightly glossy, not puddled with syrup.
Leave the muffins in the pan for about 5 minutes, then move them to a cooling rack for another 15 minutes. Sprinkle with more poppy seeds if desired and serve while warm. The muffins should have golden tops, tender centers, and a bright citrus aroma.