In small bowl, soak the mushrooms in 1 cup boiling water for 20 minutes. Remove the mushrooms and pour the liquid through a fine strainer to remove any grit. Reserve the liquid. Rinse the mushrooms, chop them, and set aside.
Chop the garlic, sprinkle it with 3/4 tsp. salt, and then mash it to a paste with the side of a chef's knife. Set aside.
In a 6-quart (or larger) Dutch oven, cook the bacon over medium heat until crisp, about 8 minutes. Transfer to a paper-towel-lined plate, crumble when cool, and set aside.
Add the onions and 1 tsp. salt to the bacon fat and cook, stirring occasionally, until softened, 6 to 8 minutes. Stir in the garlic paste, bay leaves, caraway seeds, thyme, and 1/4 tsp. pepper and cook, stirring constantly, until fragrant, about 1 minute. Add the chopped mushrooms, mushroom liquid, chicken broth, carrots, turnips, potatoes, barley, and 1-1/2 cups water. Bring to a boil over high heat; skim any foam as necessary. Reduce the heat, cover, and simmer, stirring occasionally, until the barley and vegetables are tender, 20 to 25 minutes. Add the lemon juice, season with salt and pepper, and discard the bay leaves. Serve garnished with the bacon.
You can store leftovers in the refrigerator for up to 2 days.