Combine water, milk, salt, egg, 4 tablespoons butter, and 1/2 cup sugar in a mixer bowl. Sprinkle yeast over mixture, and let stand until foamy, about 10 minutes. With mixer on low speed, add flour, beating until sticky dough forms.
Turn dough out onto a lightly floured surface, and knead until a ball forms, 3 to 5 minutes. Place in a buttered bowl, cover with plastic wrap, and let rise in a warm, draft-free spot until doubled in bulk, about 1 hour.
Butter two 9-by-13-inch glass baking dishes. Divide dough in half, and stretch 1 portion to cover 1 dish. Repeat with remaining dough and dish. Toss peach slices with lemon juice. Arrange peaches on top of dough (leaving juices in bowl), overlapping. Mix cinnamon and remaining 1 cup sugar in a small bowl. Drizzle remaining 2 tablespoons butter over peaches, and sprinkle with cinnamon sugar. Let dough rise for 1 hour.
Preheat oven to 375 degrees. Bake cakes in upper third of oven, rotating halfway through, until a tester inserted in the centers of the cakes comes out clean (bottom crusts will be golden brown), 30 to 35 minutes. Let cool completely in pans on wire racks. Cut each cake into 15 squares, and serve. (Cake can be covered and stored at room temperature for up to 2 days.)