For the strawberry sauce: Cook the strawberries, sugar, lemon juice and 2 tablespoons water in a medium saucepan over medium heat, stirring frequently, until the berries break down, about 10 minutes. Stir in the vanilla. Strain through a fine-mesh sieve into a medium bowl, pressing on the solids; let cool.
Meanwhile, for the pancakes: Whisk the flour, sugar, baking powder and salt in a large bowl. Whisk the milk, butter, eggs and vanilla in a medium bowl, then whisk into the flour mixture until just combined.
Heat a griddle or large nonstick skillet over medium heat; lightly brush with melted butter. Working in batches, pour 1/4 cup of the batter onto the griddle for each pancake and cook until bubbles form on top and the bottom is lightly browned, about 3 minutes. (If the pancakes are browning too quickly, reduce the heat to medium-low.) Flip and continue cooking until golden on the other side, about 1 more minute. Transfer to a plate. Repeat with the remaining batter, brushing the pan with more butter as necessary.
Stack the pancakes, then drizzle with the strawberry sauce and insert a knife into the top.