Cook pasta in large pot of boiling salted water until almost tender, stirring occasionally, about 6 minutes. Add asparagus and cook until pasta is tender but still firm to bite, about 3 minutes longer. Drain. Transfer to large bowl. Meanwhile, stir cream, 1 tablespoon butter, and lemon peel in heavy small saucepan over medium-high heat until mixture comes to simmer. Reduce heat to low. Whisk in 2 tablespoons cheese. Cook until sauce is smooth and thickens slightly, stirring constantly, about 1 minute. Add sauce to pasta and asparagus and toss to coat. Add remaining 1 tablespoon butter, 2 tablespoons cheese, and lemon juice; toss again to coat. Season to taste with salt and pepper. Divide pasta mixture between 2 warm bowls. Spoon salmon caviar atop pasta. Sprinkle with chives and serve.