In a 5- to 6-quart pan, bring about 3 quarts water to a boil over high heat. Snap off and discard tough ends of asparagus.
Add asparagus to boiling water. Cook, uncovered, until just barely tender to bite, 4 to 5 minutes. With tongs, lift out asparagus and drain; cool slightly.
In a blender or food processor, combine lemon juice, oil, garlic, and basil. Return water in pan to a boil.
Add fettuccine. Cook, uncovered, until barely tender to bite, about 3 minutes.
Meanwhile, diagonally trim off top 3 to 4 inches of asparagus spears.
Place asparagus tips in a colander. Coarsely chop stems and add to blender along with 6 tablespoons hot water from pasta pan. Whirl until smooth.
Drain pasta into colander containing asparagus tips.