Prepare the dough. Pour warm water into a bowl, add yeast and 1/2 teaspoon of sugar. Set aside for 2 minutes. Then add 1/3 cup flour to the water and mix well. Cover the bowl and place in a warm place for the dough to rise, about 30 minutes.
Pour milk into a saucepan and put on low heat, heat until hot, then add 1/4 cup sugar and a pinch of salt. Remove milk from heat, stir sugar, and let cool for 5 minutes, until warm. Pour milk into the bowl of the food processor or into a regular large bowl. Add eggs, mix well. Then add the dough and all the flour (3/4 cup at a time). Add the butter gradually. At the very end, add lemon zest, juice, and cranberries. Knead the dough on a floured surface for 8-10 minutes, until elastic (well-kneaded dough should not stick to your hands). Shape the dough into a ball and place in a lightly oiled bowl, cover, and place in a warm place for 2 hours (the dough should double in volume).
Cover two large rectangular baking sheets with parchment. Put the matched dough on a work surface sprinkled with flour, knead well and divide into two parts. Roll each part into a layer about 20×23 cm long. Put these layers on baking sheets, cover with paper towels, and put in a warm place for 1 hour to rise.
Turn on the oven to preheat to 190 degrees. Place the trays in a preheated oven and bake the flatbread for about 25 minutes, until golden brown.
Remove the finished flatbread from the oven, let cool on a wire rack at room temperature.
Serve flatbread with cranberries either warm or cold.