Combine water, olive oil, and 1 teaspoon salt in a large pot; bring to a boil. Cook lasagna noodles in the boiling water until tender yet still firm to the bite, about 8 minutes. Drain and rinse with cold water.
Preheat oven to 350 degrees F (175 degrees C). Grease an 8x12-inch baking dish with cooking spray.
Bring a large pot of lightly salted water to a boil. Add asparagus and cook uncovered until bright green, about 3 minutes. Transfer to a colander and rinse with cold water. Add chives to the boiling water; cook for 1 minute. Transfer to the colander and rinse with cold water.
Mix mascarpone cheese, sour cream, and Dijon mustard together in a bowl. Fold in chopped onion, capers, dill, caper brine, white pepper, and lemon zest.
Place lasagna noodles on a flat work surface. Spread 1 spoonful of mascarpone mixture down the middle of each noodle. Cover mascarpone mixture with salmon slices. Arrange 4 spears of asparagus perpendicularly over salmon. Gather up sides of the noodles to form bundles around the asparagus; tie up with chives. Transfer bundles to the prepared baking dish.
Combine Meyer lemon juice, butter, grated onion, brown sugar, dry mustard, 1/2 teaspoon salt, and black pepper in a small saucepan. Cook and stir over medium heat until sauce is smooth, 3 to 5 minutes. Pour sauce over bundles.
Bake bundles in the preheated oven until heated through, about 20 minutes. Sprinkle paprika on top before serving.