Toss pistachios, fennel seeds, and 1 tablespoon oil in a small skillet over medium heat and cook, stirring occasionally, until fragrant, about 3 minutes. Season with salt. Transfer to a small bowl; let cool. Toss fennel, lettuce, parsley, tarragon, chives, lemon zest, and horseradish in a large bowl. Add lemon juice; season with salt and pepper and toss to coat. Add remaining 1/4 cup oil and toss to coat, then add half of pistachio mixture and toss just to combine. Season with salt, pepper, and more lemon juice, if desired. Serve salad topped with remaining pistachio mixture. Do ahead: Pistachio mixture can be made 2 days ahead; store tightly wrapped at room temperature.