In a large Dutch oven or large pot, heat the oil over medium heat. Add the diced pancetta and cook for 5-7 minutes until golden brown and crisp. Use a slotted spoon to transfer the pancetta to a small dish lined with paper towels to drain excess oil.
In the same pot, add the sliced leeks, minced garlic, chopped asparagus, diced potatoes, and thyme. Season with salt and pepper. Cook for about 5 minutes until the leeks are translucent and fragrant.
Pour in the broth and bring the mixture to a boil. Reduce the heat to low and let the soup simmer for 20 minutes on medium-low heat or until the potatoes are fork-tender.
Using a blender, carefully blend the soup in batches until it has a smooth texture. Return the blended soup to the Dutch oven.
Stir in the heavy cream and fresh lemon juice. Season with additional salt to taste, if needed.
To serve, ladle the soup into bowls. Top each serving with the crispy pancetta, a drizzle of additional cream, and a sprinkle of chopped chives.