In a small saucepan, bring the stock, leek, porcini, lemon slices, and bay leaf to a boil. Reduce heat enough to keep at a low rolling simmer. Cook for 20 minutes to reduce and infuse the stock.
Bring a large pot of water to a boil for the pasta.
Heat a large skillet over medium-high to high. Add the oil, four turns of pan. Add the fresh mushrooms and thyme and cook, stirring occasionally, until fragrant and browned, about 5 minutes. Add the celery, shallots, and garlic; season with salt and pepper. Cook, stirring often, until the vegetables soften, 3 to 5 minutes. Add the wine and cook, stirring occasionally, until absorbed, about 3 minutes.
Salt the boiling water and add the pasta. Cook until 1 minute shy of the package directions. Drain the pasta.
Strain the stock, leaving any grit from the porcini behind in the pan. Add the stock to the mushroom mixture. Toss the pasta, walnuts, cheese, and parsley with the mushroom mixture; season. Serve in shallow bowls.