Heat 2 tablespoons butter in a large Dutch oven or pot over medium-high heat. Add the chopped celery stalks, endive, shallots, garlic, 1/2 teaspoon salt and a few grinds of pepper; cook, stirring, until the vegetables are softened, 4 to 5 minutes. Increase the heat to high and stir in the mussels and thyme. Add the wine and bring to a boil; cover and cook, shaking the pot occasionally, until the mussels open, 3 to 5 minutes. (Discard any unopened mussels.)
Transfer the mussels and vegetables to a bowl using a slotted spoon. Whisk the remaining 6 tablespoons butter and the lemon juice into the liquid in the pot. Bring to a boil, then remove from the heat and return the mussels to the pot. Sprinkle with celery leaves and parsley; toss to coat. Serve with toasted baguette.