Bring a large pot of salted water to a boil and fill a large bowl with ice water.
Add the asparagus to the boiling water and cook until just tender, 1 to 2 minutes. Drain and transfer to the ice water. Once cooled, drain and pat dry and add to a medium bowl.
Heat the oil in a small saucepan over medium heat, add the walnuts and garlic and cook, stirring occasionally, until just golden, 1 to 2 minutes. Pour mixture over the asparagus and toss to combine. Season to taste with salt and pepper.
To serve, transfer asparagus to a platter and scatter Parmesan on top. Drizzle with lemon juice and serve immediately.