Preheat oven to 350 degrees. Place red beets in a baking dish just large enough to hold them in a single layer and add enough water to come three quarters of the way up sides of beets. Sprinkle with 1 tablespoon salt and drizzle with grapeseed oil. Cover with foil and bake until tender and easily pierced with a knife, about 1 hour. Transfer beets to a cutting board. When just cool enough to handle, remove skins, cut into 1/4-inch slices, and transfer to a bowl.
Meanwhile, place baby beets in small saucepan and cover with 2 inches cold water. Add 1 teaspoon salt and bring to a boil. Reduce heat and simmer until tender and easily pierced with a knife, about 25 minutes. Drain beets; when just cool enough to handle, remove skins; cut into halves or wedges, depending on size; and transfer to another bowl.
Whisk together honey, olive oil, and 3 tablespoons lemon juice; add 1 teaspoon salt and season with pepper. Reserve 1/4 cup dressing; divide remaining dressing between bowls of warm beets; toss beets to coat.
Halve lemon and squeeze juice into a bowl of cold water; drop lemon halves in it. Peel apple, cut into small pieces (you should have about 1 cup), and submerge in lemon water. When ready to serve, drain apple and blot dry. Arrange beets on a serving platter and drizzle with reserved dressing. Top with apple, goat cheese, and sprouts and serve immediately.