Heat olive oil in a large pot over medium heat. Add onion and cook 4 to 5 minutes until soft and translucent.
Add garlic and cook 30 seconds until fragrant.
Add celeriac and apple, stir to coat in the oil, and cook 3 minutes.
Pour in the stock, add thyme, and bring to a boil. Reduce to a simmer, cover, and cook 20 to 25 minutes until the celeriac is fork-tender.
Remove the thyme sprigs. Blend with an immersion blender for 30 to 45 seconds until smooth, or blend in batches in a stand blender.
Stir in the milk or crème fraîche, lemon juice, salt, and pepper. Warm through 2 to 3 minutes without boiling.
Ladle into bowls and garnish with chives or raw apple matchsticks.