Heat olive oil in a large pot over medium heat. Add the chopped onion and garlic, and cook for about 4 minutes until softened. Add the asparagus, season with salt and pepper, and cook for another 3 minutes.
Pour in the vegetable broth and bring the mixture to a boil. Lower the heat and simmer for 15 minutes until the asparagus is tender.
Use an immersion blender to purée the soup until smooth. Stir in the low-fat milk, sour cream, and fresh lemon juice. If the soup is too thick, add a bit more milk or broth to correct the consistency.
Warm the soup over low heat, avoiding boiling, and then serve it hot. Garnish with freshly ground black pepper, chopped chives, and some Parmesan cheese if desired.