Prepare creamy eggs by whisking with milk, chives, salt, and pepper. Melt butter in a nonstick skillet over medium heat. Reduce heat to low, add eggs and stir constantly, scraping the sides and bottom of the pan until eggs are creamy and thickened.
Make dill sour cream. Mix sour cream, capers, dill, lemon juice and zest. Stir and add salt and pepper to taste. Keep refrigerated until using.
Spread lox onto basic crepes and top with creamy scrambled eggs. Fold the crepes and top with dill sour cream.