How to Make It
Combine yeast, 1/4 cup of the warm water, and 1 teaspoon of the sugar in the bowl of a stand mixer. Let stand until foamy, about 5 minutes. Add milk, butter, lemon zest, juice, 2 cups of the flour, 3 of the eggs, and remaining 1/2 cup sugar; beat on low speed with a paddle attachment just until combined and smooth, about 1 minute. Replace paddle with a dough hook, and with mixer on medium speed, gradually add remaining flour. Mix on medium-low until dough pulls away from the sides but still tacky, about 3 minutes.
Turn dough out onto a clean work surface lightly dusted with flour. Sprinkle poppy seeds over dough. Knead until dough is smooth and only the slightest amount of tack remains, about 4 minutes. Transfer dough to a bowl coated with cooking spray, turning to coat all sides of dough. Cover with plastic wrap; let rest at room temperature until doubled in bulk, about 1 hour and 30 minutes.
Turn dough out onto work surface and separate into 2 equal portions. Working with 1 piece at a time, cut into 3 equal portions and shape each into a 15-inch long rope. Place ropes about 1-inch apart and braid together, finishing by pinching ends of braid together and tucking under. Transfer to a baking pan lined with parchment paper. Repeat process with remaining portion of dough. Cover loosely with plastic wrap; let stand at room temperature until almost doubled in bulk, 1 hour to 1 hour and 15 minutes.
Preheat oven to 375ºF. Whisk together remaining egg and 1 teaspoon water in a small bowl. Brush evenly over bread, and bake in preheated oven until golden brown, about 22 minutes. Transfer pan to a wire rack to cool completely, about 45 minutes.