Preheat the oven to 400 degrees F. Cover the lentils with 2 inches of water in a medium saucepan; add 3/4 teaspoon salt, a few grinds of pepper and the bay leaves. Bring to a boil, then reduce the heat and simmer until tender, 20 to 25 minutes. Drain, discarding the bay leaves.
Meanwhile, thinly slice the red onion and toss with the vinegar in a large bowl; set aside. Combine the bread and tarragon in a food processor and process into coarse crumbs. Season the chicken with salt and pepper and brush one side with the mustard. Press the crumbs onto the mustard in a thick layer.
Heat a large ovenproof nonstick skillet over medium heat. Add the butter and let melt. When the foaming subsides, add the chicken crumb-side down and cook, undisturbed, until browned and crisp, 5 to 7 minutes. Carefully flip the chicken and transfer the skillet to the oven. Bake until cooked through, 11 to 13 minutes.
Add the warm lentils, spinach and olive oil to the bowl with the red onion; stir until the spinach wilts. Serve with the chicken.