Bring a large pot of salted water to a boil. Add the asparagus and cook until it is crisp-tender, about 2 to 4 minutes, depending on the thickness of the asparagus. Using a slotted spoon, lift the asparagus out of the boiling water and plunge it into a bowl of ice water. Drain.
Bring the large pot of water back to a boil, add the fettuccine and cook until it is al dente, about 10 to 12 minutes. Drain.
Meanwhile, bring the chicken broth and shallots to a boil in a large skillet. Cook until the broth has reduced by half. Add the lemon juice and lemon zest. Whisk in the sour cream.
Add the drained asparagus and fettuccine to the sour cream sauce and toss to combine. Season with salt and pepper.
Divide the fettuccine and asparagus among 4 warm bowls and sprinkle with Parmesan cheese.