Squeeze 1/2 tsp juice from lemon into a medium-size bowl. Whisk in sour cream, shallots, oil, water, tarragon, salt and paprika. Taste and add more lemon juice, if needed. If making ahead, cover and refrigerate up to 2 days. Bring to room temperature before using.
Meanwhile, fill a wide saucepan with about 2 inches water. Add vinegar and bring to a boil over high heat. To cook bacon, lightly oil a large frying pan and set over medium-high heat. Add bacon. Cook until golden tinged, about 1-2 min per side. Remove pan from heat.
Once water boils, reduce heat to low so water is barely simmering. Crack an egg into a small dish, then slip into water. Repeat with remaining eggs. Simmer, uncovered, until whites are set and yolks are done as you like. 2-4 minute To serve, place 1-2 pieces of bacon on an English muffin half. Using a slotted spoon, remove eggs one at a time and dab whites with paper towel to absorb as much water as possible. Place 1 egg on top of the bacon. Repeat with remaining eggs. Spoon about 1 1/2 tbsp sauce over each egg, sprinkle with chives.