Melt butter in a small frying pan over medium heat. Add onion and cook, stirring, until soft but not browned, about 3 minutes. Let cool slightly.
Scrape onion into a food processor and add hot- and cold-smoked salmon. Pulse mixture until fish is coarsely chopped. (Do not overblend, or mixture will become pasty.)
Scrape into a medium bowl and gently stir in crème fraîche, chives, and lemon juice. Season to taste with pepper.
Note: Nutritional analysis is per 3-Tbsp. serving.