Heat the olive oil over medium high heat in a large skillet or soup pot. Add the onions and sauté for about 7 minutes, stirring now and then.
Add the chopped celery and carrots to the onions and continue to sauté the vegetables for another 7 minutes.
Add the garlic and 1 teaspoon of dried thyme and stir for an additional minute.
Add the beef broth, stirring to remove any pieces stuck to the bottom of the pan. Add the lentils and raise the heat to high. Once the soup has come to a boil, reduce the heat to simmer. If any scum appears on the surface, carefully skim it off and discard.
Partially cover the pot and cook at a simmer for about an hour.
Add the sliced mushrooms to the soup and continue cooking, partiallly covered, over low heat another 30 minutes.
When the soup is near its finished cooking time, finely chop the parsley and thyme and transfer to small bowl. Add the lime zest and lime juice and stir to combine. Set this herb mixture aside to use later.
Taste the soup to ensure that the lentils are soft. If so, use a potato masher or other implement to crush some of the lentils and create a creamy base within the soup.
Add the diced smoked turkey and cook until heated through, about 5 minutes.
Stir the herb mixture into the soup. Season with salt and pepper, if needed.
Ladle into bowls and serve.