At least 1 hour before cooking, and up to 24 hours ahead for best results, pat the chicken dry and season it all over with the kosher salt. Set it uncovered on a rack in the fridge if brining longer than an hour.
Preheat the oven to 425°F (220°C). Set a wire rack inside a rimmed sheet pan.
Toss the fennel wedges with olive oil and salt, and spread them on the sheet pan beneath where the rack will sit.
Pat the chicken dry again, rub it with the oil and pepper, and arrange it skin-side up on the rack above the fennel. Nestle the lemon halves, cut-side down, among the fennel wedges.
Roast for 40 to 45 minutes, until the skin is deep golden brown and the thighs and drumsticks reach 175°F (79°C) internally.
While the chicken roasts, whisk together the soy sauce, lemon juice, lime juice, rice vinegar, and honey, adding the kombu if using. Let it sit at room temperature, then remove the kombu before serving.
Rest the chicken for 5 minutes off the rack. Squeeze the roasted lemon halves over the fennel, stir the scallions and sesame oil into the sauce, and spoon it over the chicken and fennel just before serving.