Preheat oven to 375 degrees. Bring lemon juice to a simmer in a small saucepan over medium heat; cook until reduced by half. Add 1 stick butter; stir until melted.
Whisk together flour, baking powder, and salt. Cream remaining stick butter and 1 cup sugar on medium speed in the bowl of an electric mixer fitted with the paddle attachment. Mix in egg and lemon butter. Mix until pale, about 3 minutes. Mix in vanilla and 2 teaspoons zest. Mix in flour mixture and poppy seeds.
Stir together remaining 1/2 cup sugar and 1 1/2 teaspoons zest. Roll spoonfuls of dough into 1 1/2-inch balls; roll them in sugar mixture. Place 2 inches apart on baking sheets. Press each with the flat end of a glass dipped in sugar mixture until 1/4 inch thick. Sprinkle with seeds.
Bake until just browned around bottom edges, 10 to 11 minutes. Transfer to wire racks; let cool completely. Store in an airtight container up to 1 week.