Heat the oil in a large pot over medium heat. Add the onions and the mushrooms and cook for 2-3 minutes until they begin to soften.
Add the dill, paprika, soy sauce, and ½ cup of stock. Stir to combine and then cover with lid. Reduce heat to low and simmer for 15 minutes. Transfer the mushroom mixture and the liquid from the pot to a bowl and set aside.
Return the pot to the stove over medium heat and melt the butter in it. Add the cornstarch and whisk smooth. Slowly add the milk while whisking constantly. When the milk mixture is smooth, add the remaining chicken stock while whisking constantly.
Add the mushroom mixture back into the pot along with the rest of the stock. Bring to a simmer. Use a ladle or a small measuring cup to remove a small amount of broth (about ½ cup) from the pot and then whisk the sour cream into it.
Add the sour cream mixture back to the pot and stir to combine. Add the lemon juice and season to taste with salt and pepper.