Preheat the oven to 350°F. Butter and flour a 12-cup Bundt pan, tapping out the excess flour. In a food processor, pulse together the flour, sugar, poppy seeds, baking powder, and salt. Add the butter and pulse to form pebble-size pieces.
Whisk together the yogurt, eggs, and lemon zest. Add to the flour mixture and pulse until just combined, 30 seconds. Spoon the batter into the prepared pan and bake until the cake is light golden brown and a toothpick inserted in the center comes out clean, 30 to 35 minutes.
Meanwhile, make the syrup. Combine the sugar and 3 tablespoons water in a small pan. Cook over low heat until the sugar has dissolved and is just warm (do not boil). Stir in the lemon juice.
Cool the cake in the pan on a rack, 20 minutes, then turn out onto a serving platter; cool until just warm to the touch. Prick all over with a toothpick. Slowly drizzle the syrup over the cake. Cut into slices and serve.