Toast the bagel halves until golden brown. Meanwhile, dress the smoked salmon with the lemon juice in a small mixing bowl. Soften the cream cheese using a spoon in a mixing bowl and spread onto the bottom half of the toasted bagels.
Arrange the slices of smoked salmon evenly on top of the cream cheese and sprinkle over the chopped chives. Transfer to serving plates.
Place a few chive stalks on top of the smoked salmon and rest the toasted top halves of the bagels on top, to the side. Serve immediately.