Combine the sour cream, water, arrowroot, and paprika in a small bowl. Whisk until a thick paste forms. Set aside.
Using a stock pot or dutch oven, melt the butter over medium heat. Add the onion, carrots, and celery and saute for 5 minutes. The vegetables should be lightly fork-tender.
Add the mushrooms and saute until they are softened, for about 5 more minutes. Season with salt, pepper, and dill, and stir to coat the vegetables.
Add the chicken broth to the pot and stir well to combine. Bring the broth to a low boil before adding the sour cream paste and stirring to combine.
Reduce to a medium simmer for 10-15 minutes, stirring often until the soup is thickened and flavorful.
Squeeze in fresh lemon juice and garnish with fresh chopped parsley.