Heat 1 ½ tablespoons of the oil in a large soup pot. Add the onions and sauté over low heat until they begin to turn golden.
Add the garlic, turnips or parsnips, celery, tomatoes and liquid, and about two-thirds of the carrots. Set aside the remaining carrots.
Stir in 2 cups water and the seasonings and bring to a simmer. Cover and simmer gently until the vegetables are tender but not mushy, about 25 to 30 minutes. Remove from the heat.
With a slotted spoon, transfer the cooked vegetables, along with a little of the cooking liquid, to a food processor. Process in batches to a smooth consistency and return the puree to the soup pot. Or, simply insert an immersion blender into the soup pot and puree until smooth.
Stir in enough rice milk to give the soup a medium-thick consistency. Return to low heat.
Heat the remaining oil in a small skillet. Sauté the reserved carrots over medium heat until golden and nearly tender. Stir them into the soup, then season to taste with salt and pepper.
Stir in the parsley and lemon juice and serve once the soup is well heated through.