Preheat oven to 300 degrees. Heat 1/4 cup oil in a Dutch oven over medium-high heat. Season ribs with salt and pepper. Working in batches, brown ribs, 3 to 4 minutes per side; set aside.
Add 1 onion, and reduce heat to medium. Cook, stirring, until softened, 5 to 6 minutes. Return ribs to Dutch oven, and add wine; simmer for 1 minute. Add chicken stock; bring to a simmer, and season with salt and pepper. Cover; transfer to oven, and roast until ribs are tender, 3 hours.
Shred ribs, discarding fat and bones. Strain stock through a sieve, and skim off fat. (You should have 2 cups.)
Heat remaining 2 tablespoons oil in Dutch oven over medium heat. Add remaining onion and the garlic; cook until translucent, about 4 minutes. Add celery root and carrots; cook for 4 minutes. Add reserved stock, the cabbage, beets, water, and tomato paste. Cook for 30 minutes. Add meat; cook until vegetables are tender, about 20 minutes more. Stir in lemon juice and vinegar; garnish with parsley.
Borscht can be refrigerated for up to 5 days.