Set the Instant Pot to the sauté setting on high for 3 minutes. When the insert is hot, add the olive oil, followed by the onion, garlic, and potato. Cook, stirring often, until the vegetables begin to soften and nothing sticks to the bottom.
Pour in the vegetable broth and use a wooden spoon to scrape up any browned bits from the base of the pot. Add the asparagus, setting aside 6 to 8 pieces for garnish. Stir in the thyme, basil, salt, and black pepper, then secure and seal the lid.
Cook on high pressure for 5 minutes. Once the cooking cycle ends, perform a controlled quick release. After all pressure has been released, open the lid carefully.
Blend the soup in the pot with an immersion blender until fully smooth. Stir in the lemon juice, then taste and adjust the seasoning as needed.
Using tongs, dip the reserved asparagus pieces into the hot soup for 10 to 20 seconds to lightly cook them. Ladle the soup into serving bowls and top each portion with the reserved asparagus. Finish with extra basil and a pinch of red pepper flakes, if desired.