Preheat the oven to 375 degrees F and spray a 13×9 casserole dish with cooking spray. Cook the egg noodles according to package directions and set aside.
In a large skillet over medium heat, melt 1 Tbsp. butter. Sauté the onions until golden and translucent, season with salt and pepper. Add the mushrooms and cook until the mushrooms have shrunk and cooked through. Add 1 Tbsp. of the soy sauce and stir well. Remove from heat and set aside.
Place the skillet back on the range over medium-high heat, add the remaining 2 Tbsp. butter and 2 Tbsp. olive oil. Whisk in the flour and cook for two minutes, then slowly add the chicken broth, whisking constantly. Bring to a boil, then whisk in the milk. Reduce the heat to a simmer and cook for another 5 minutes.
Add the mushroom and onion mixture to the white sauce and then stir in the lemon juice. Add the rest of the soy sauce (2 tsp.), drained tuna, peas, and the cooked egg noodles.
Transfer the mixture to the casserole dish. Top with the cheddar cheese and breadcrumbs. Bake for 15-20 minutes, until the breadcrumbs are toasted and cheese is melted.