Yes, there is butter in the sauce, but the key ingredient is verjus. If you can't find it, use half white wine and half unseasoned rice vinegar.
Ingredients
2 tablespoons olive oil
1 small carrot, peeled, finely chopped
1 celery stalk, finely chopped
1/2 small onion, finely chopped
2 garlic cloves, finely chopped
1 cup black beluga lentils or French green lentils
2–3 cups low-sodium chicken broth
2 teaspoons Sherry vinegar
Kosher salt, freshly ground pepper
1 small shallot, thinly sliced
1 garlic clove, peeled, crushed
1 whole star anise pod
1 bay leaf
6 black peppercorns
1 cup white verjus
1/2 cup dry white wine
1/2 cup (1 stick) chilled unsalted butter, cut into pieces
1 tablespoon chopped fresh tarragon
1 tablespoon fresh lemon juice
Kosher salt, freshly ground pepper
2 tablespoons olive oil
4 6-ounce skin-on steelhead trout or salmon fillets
Kosher salt, freshly ground pepper
1 tablespoon unsalted butter
2 tablespoons chopped fresh flat-leaf parsley
Ingredient info: Verjus is a tart juice made from unripe grapes. Find it at specialty foods stores and online.
Directions
Heat oil in a large saucepan over medium-high heat. Add carrot, celery, onion, and garlic and cook, stirring often, until softened, 5–8 minutes. Mix in lentils and add broth to cover by 1". Bring to a boil; reduce heat, cover, and simmer, adding more broth as needed to keep lentils covered, until lentils are tender, 20–30 minutes. Mix in vinegar; season with salt and pepper. Cover and set aside; keep warm.
DO AHEAD: Lentils can be cooked 1 day ahead. Let cool; cover and chill.
Bring shallot, garlic, star anise, bay leaf, peppercorns, verjus, and wine to a boil in a medium saucepan and cook until reduced to 1/4 cup, 15–20 minutes. Strain through a fine-mesh sieve into a small saucepan; discard solids.
Place saucepan over low heat and gradually whisk in butter, until butter is melted and sauce is emulsified. Whisk in tarragon and lemon juice; season with salt and pepper. Cover and set aside; keep warm.
Heat oil in a large nonstick skillet over medium-high heat. Season fish with salt and pepper. Place fish, skin side down, in pan and cook, undisturbed, until skin is crisp and releases from pan, about 4 minutes. Turn fish, add butter to pan, and cook, tilting pan and spooning butter over fish, until opaque throughout, about 2 minutes longer.
Stir parsley into verjus beurre blanc just before serving. Serve fish with lentils and sauce.