Heat the oil in a large pot over medium heat. Add the onions and cook for a couple minutes. Add the mushrooms, soy sauce, dill, paprika and about 1/2 a cup of stock. Stir to combine and then cover with lid. Simmer for 15 minutes. Remove the mushroom mixture and liquid from the pot to a bowl and set aside.
Place the pot back on the stove over medium heat and melt the butter in it. Add the arrowroot and whisk until creamy. This should only take about a minute. Slowly add the milk while whisking constantly. Cook, stirring constantly, until the mixture thickens, about 5 minutes.
Add the mushroom mixture back into the pot along with the rest of the stock. Cover with the lid and simmer another 10 minutes or so. Just before serving, add the lemon juice and season with salt and pepper. Remove a small amount of broth from the pot and whisk the sour cream into it. Add this mixture back into the pot and stir to combine. Enjoy!