Melt butter in a large sauté pan or skillet over medium heat; cook, stirring often, 5 minutes or until butter turns medium brown with a nutty aroma. Add leeks and cook, stirring often, 5 to 7 minutes or until very tender.
Add mussels and lemon juice. Increase heat to medium-high and cook, shaking pan occasionally, 3 to 5 minutes or until mussels open. (Discard any that do not.) Add fettuccine, chives, and pepper to pan, tossing well.