Preheat the slow cooker if necessary; see the manufacturer's instructions. Brush inside the slow cooker pot with a little of the butter. Fold a large piece of kitchen foil into 3, then place it at the bottom of the pot with the ends sticking up to use as a strap. Arrange the onion slices and half of the lemon slices over the foil. Place the salmon, flesh side up, on top. Season with salt and pepper, then add the bay leaf and remaining lemon slices.
Pour the wine and stock into a saucepan, bring to the boil, then pour over the salmon. Fold the foil down if necessary to fit the cooker lid, then cook on low for 1¾–2¼ hours until the fish is opaque and flakes easily when pressed in the centre with a knife.
Lift the salmon carefully out of the pot using the foil strap, draining off as much liquid as possible. Transfer to a serving plate, discard the bay leaf, lemon and onion slices, and keep warm. Strain the cooking liquid into a saucepan and boil rapidly for 4–5 minutes or until reduced to about 4 tablespoons.
Reduce the heat and gradually whisk in small pieces of the remaining butter, little by little, until the sauce thickens and becomes creamy. (Don't be tempted to hurry making the sauce either by adding the butter in one go or by increasing the heat to the sauce, or you may find that it separates.) Stir in the chopped chives and adjust the seasoning if needed.
Cut the salmon into 4 portions, discard the skin and transfer to individual plates. Spoon a little of the sauce around the fish. Garnish with lemon slices and chives.