Preheat oven to 425 degrees, with rack in the middle. In a large saucepan, heat butter over medium. Add carrot, onion, fennel, and fennel seed. Cook until carrot is crisp-tender, 8 to 10 minutes. Add flour; cook, stirring, 1 minute. Gradually add milk and broth, stirring until smooth. Cook, stirring occasionally, until mixture comes to a simmer and thickens, 5 to 8 minutes.
Remove from heat; stir in chicken, ham, and lemon juice; season with salt and pepper. Divide filling among eight 8-ounce ramekins or ovenproof bowls; set aside.
On a floured surface, roll out dough to a 15-inch round. With a 3 1/2-inch floured biscuit cutter, cut out eight rounds; place one on each ramekin. Transfer ramekins to a rimmed baking sheet; bake until filling is bubbling and crusts are golden, 20 to 25 minutes. Let cool 5 minutes before serving.
To store: Prepare through step 3; let cool to room temperature. Cover with plastic wrap, then aluminum foil; store in freezer, up to 3 months.
To reheat: Preheat oven to 425 degrees. Uncover ramekins; bake on a rimmed baking sheet until bubbling and golden, 30 to 35 minutes. Let cool 5 minutes before serving.