Combine chicken broth, onion, parsley, lemon, salt, and pepper in a large skillet. Bring to a boil. Add salmon to the skillet in a single layer. Bring back to a boil. Reduce heat, cover, and simmer until salmon flakes easily with a fork, 5 to 10 minutes. Remove salmon from the skillet and keep warm.
Strain cooking liquid and reserve 2 cups.
Melt butter in a small saucepan over medium heat. Whisk in flour, dill, sugar, and salt. Cook until bubbling, about 1 minute. Add reserved cooking liquid. Cook, whisking constantly, until sauce begins to thicken.
Slowly stir 1/2 cup sauce into the egg yolks. Pour back into the saucepan. Cook, stirring constantly, until thick, 1 to 2 minutes. Do not boil. Stir in lemon juice. Spoon sauce over salmon. Serve remaining sauce alongside.
