Preheat oven to 425 degrees Fahrenheit.
Rinse and pat dry the game hens and squab. With your fingers, gently loosen the skin all over, making a pocket between the skin and the breast meat. Place proscuitto slices and a few slices of black truffle in between the breast meat and skin. Season the central cavity with salt and pepper. Stuff the inside of each cavity with a clove of garlic, a sprig of thyme and a lemon wedge. With butcher’s twine, truss the birds and season the outside generously with salt and pepper.
Heat vegetable oil in a couple of large skillets over medium high heat. Brown each bird on all sides and transfer into roasting pans (keeping the game hens and squab separate). Place both pans in the oven and roast, basting the birds occasionally with pan juices, until the birds are browned and until the juices run clear when the inner thigh is pierced (the temperature in the thigh should be 155 degrees Fahrenheit). Cover with foil and keep warm while allowing meat to rest before carving.