Heat grapeseed oil over medium heat in a large pot and add onion and garlic, sauteing them until they are translucent. Add beets and cucumber, and cover with 6 cups water. Season with salt and pepper. Bring to a boil and cook until tender, about 45 minutes. Remove from heat and bring to room temperature.
Add orange juice and blend with an immersion blender, or in batches in a conventional blender. Season with salt and pepper, to taste. Stir in lime juice and chill.
Spoon into serving bowls, garnish with a dollop of sour cream and sprinkle with dill pickle.