Heat coconut oil in a large pot over medium heat; sauté diced onion until translucent, about 5 minutes.
Add minced garlic and chopped ginger; cook for 1-2 minutes until fragrant.
Add diced beets and salt; stir well to combine.
Pour in vegetable stock; bring to a boil, then reduce heat and simmer until beets are tender, about 20-25 minutes.
Using an immersion blender or regular blender, blend soup until completely smooth.
Stir in coconut milk; heat gently for 2-3 minutes.
Adjust seasoning with additional salt and add lemon or lime juice if using.