For the bechamel: Melt the butter in a large saucepan over medium heat. Whisk in the flour to form a smooth paste. Cook, whisking constantly, for 3 minutes. Slowly whisk in the milk until smooth. Add the salt and bay leaf and bring the mixture to a simmer, whisking occasionally. Reduce the heat to low and simmer, stirring occasionally to prevent burning, for 20 minutes. Remove and discard the bay leaf.
For the lasagna: Meanwhile, add the oil and bacon to a large skillet over medium heat and cook, stirring often, until the bacon is crispy and golden brown and the fat is rendered, about 15 minutes. Using a slotted spoon, remove the bacon to a paper towel lined plate. Drain off all but 3 tablespoons of the fat from the skillet. Add the mushrooms and 1 teaspoon salt to the skillet and increase the heat to medium-high. Cook, stirring occasionally with a wooden spoon, until the mushrooms have released their liquid and are beginning to brown, about 15 minutes. Add the onion, carrot, celery, garlic, thyme and remaining 1 1/4 teaspoons salt and cook until fragrant, the vegetables are soft and the mushrooms have browned, about 5 minutes longer. Deglaze with the white wine. Simmer until the liquid is almost entirely evaporated, about 4 minutes. Stir in the reserved bacon.
Preheat the oven to 400 degrees F. Butter a 9-by-13-inch baking dish.
Ladle and spread 1 cup bechamel on the bottom of the baking dish. Place a layer of pasta over the bechamel, breaking the pasta to fit the pan if needed. Spread 1 1/2 cups bechamel over the pasta. Spoon half of the mushroom filling over the bechamel and top with 3/4 cup Parmesan. Place another layer of pasta on top of the filling and repeat with the bechamel, the remaining mushroom filling and another 3/4 cup Parmesan. Layer on another layer of pasta and top with the remaining bechamel and Parmesan.
Bake until golden brown and bubbly around the edges, 30 to 35 minutes. Allow the lasagna to rest for 15 minutes before serving.
This makes a 3-layer lasagna. If you would like more layers, simply switch to a slightly smaller baking dish and layer up!