Grease or line 12 cups of a standard-size muffin pan. Set aside.
Whisk flour, 1/4 cup sugar, baking powder, baking soda, and salt in a large bowl. Set aside.
In a separate bowl, whisk together butter, lemon zest, lemon juice, vanilla extract, and eggs. Stir the wet mixture into the dry ingredients until just moistened. Add a spoonful of batter to each of the prepared muffin cups.
Toss raspberries with 1 tablespoon sugar in a small bowl and divide them between the muffin cups. Sprinkle any sugar remaining in the bowl over the raspberries in the pan. Top the raspberries with remaining batter. Don't worry if the raspberries aren't covered completely. Bake in an oven preheated to 400° F until lightly browned around the edges and springy to the touch, 20 to 25 minutes.
While the muffins bake, prepare the syrup. Combine lemon juice and sugar in a small saucepan. Warm over low heat until sugar just dissolves.
Spoon lemon syrup over the muffins as soon as you remove them from the oven. Cool completely in the pan to allow syrup to absorb.