Heat oven to 425°F; foil-line 18-by-13-inch rimmed sheet. Toss fennel with 1/2 tablespoon oil and 1/4 teaspoon salt; spread across center.
Pat chicken dry; rub with remaining oil, zest, garlic, thyme, pepper, and remaining salt. Set skin-side up with fennel around pieces.
Roast 25 minutes. Mix beans with 1 tablespoon lemon juice and measured water; spoon around chicken. Turn exposed fennel.
Roast 15 to 20 minutes more until thickest breast reaches 165°F and fennel tender. Check away from bone.
Rest chicken 5 minutes. Drizzle remaining lemon juice over beans and fennel; serve 1 breast half with half vegetables and beans per portion.