A pinch of allspice adds warmth to this medley of carrots and parsnips.
Preheat oven to 375 degrees, with rack in lower third. Brush a 2 1/2-quart souffle dish with butter, then coat with sugar.
Bring parsnips, carrots, and carrot juice to a boil in a medium saucepan. Reduce heat to medium-low and simmer, partially covered, until vegetables are very tender, 15 to 18 minutes. Drain, reserving 1/2 cup liquid. Puree vegetables, reserved liquid, and 1 1/2 teaspoons salt in a blender until smooth. Transfer to a large bowl.
Melt butter in a medium saucepan over medium. Whisk in flour. Cook, whisking constantly, until mixture is golden and nutty-smelling, 2 to 3 minutes. Slowly whisk in milk (mixture will splatter) and cook, whisking constantly, until mixture thickens to a paste, about 1 minute. Stir into vegetable puree along with yolks, lemon juice, thyme, and allspice. Let cool completely.
Beat egg whites on medium-low speed until foamy, about 1 minute. Increase speed to medium-high and slowly add sugar, beating until stiff, glossy peaks form, 4 to 5 minutes. Stir one-third of egg-white mixture into carrot mixture until thoroughly combined. Gently fold in remaining egg-white mixture just until combined. Transfer to prepared dish; gently smooth top.
Bake souffle until puffed and golden brown on top and center is set, 50 to 55 minutes; serve.