Put the bacon in a large skillet and set the skillet over medium heat. Cook until the bacon has begun to crisp and is half-cooked, about 8 minutes.
Add the leeks and increase the heat to medium high. Cook, stirring frequently, until the leeks are soft (the bacon will continue to crisp), about 6 minutes. Using a slotted spoon or skimmer, transfer the bacon and leeks to a bowl, leaving the fat in the pan.
Add the mushrooms to the pan and cook quickly, stirring occasionally, until the mushrooms are browned, about 6 minutes. Add the salt, lemon zest, thyme, and the leek and bacon mixture. Add pepper generously to taste (about 10 grinds) and stir.
Add the stock to the pan and bring to a boil, stirring to scrape the bottom of the pan. Cover the pan and reduce the heat to medium low. Braise slowly until the mushrooms are very tender and the liquid is absorbed, about 20 minutes. If the mushrooms are tender but still brothy, raise the heat and boil, uncovered, until the broth has reduced considerably. Taste a mushroom and add more salt and pepper if needed.