In a large bowl, combine the first 5 ingredients. Stir in eggs until blended. Add potatoes; toss to coat.
Heat 2 tablespoons oil in a large nonstick skillet over medium heat. Drop batter by 1/4 cupfuls into oil; press lightly to flatten. Fry in batches until golden brown on both sides, using remaining oil as needed. Drain on paper towels. Serve with lox; top with sour cream and chives if desired.