Add olive oil to a large pot set over medium-high heat. Add mushrooms and sauté, stirring frequently until brown, about 10 minutes. Add onion, thyme, salt and pepper and continue to cook until onions have softened, about 5 minutes.
Add butter and melt completely. Sprinkle over flour and cook, stirring constantly for 2 minutes. Gradually whisk in milk and broth. Bring to a boil and reduce heat. Simmer for 15 minutes.
Before serving, stir in lemon juice and season, to taste, with more salt and pepper. Serve garnished with fresh thyme.