Clean asparagus and cut into 2 pieces. Reserve tips for garnish.
Prepare potatoes, peel and cut into 2 pieces.
Heat oil and butter over medium heat in a large sauce pan. Add leeks or onions, stirring occasionally until soft. About 5 minutes.
Add potatoes and asparagus, cook until well coated and begin to soften, about 3 minutes.
Add chicken broth, salt and pepper; heat to a boil. Reduce heat to low; partially cover. Cook until vegetables are tender, 15 minutes.
Meanwhile, if desired, boil water over high heat (for asparagus tips). Add the tips to the boiling water; boil until tender and still green. About 3 minutes. Drain and set aside for garnish. Toss into a bowl of ice water to stop the cooking if desired.
Puree in small batches in a blender or sue a hand blender.
Stir in lemon juice to taste.
Ladle into bowl, top with a dollop of sour cream, tips, chives or croutons.