Season chicken and refrigerate overnight: Place chicken on a large plate and season generously with salt and pepper; cover with plastic wrap and refrigerate overnight.
Preheat oven, bring chicken to room temperature, and prep vegetables: Preheat oven to 450°F. Let chicken stand at room temperature 30 minutes. Meanwhile, toss carrots, shallots, potatoes, and lemon with 2 tablespoons oil; season with salt and pepper.
Arrange vegetables in roasting pan: Arrange in a large roasting pan, with shallots in center and carrots, potatoes, and lemon toward edges.
Prep chicken: Rub chicken with remaining 1 tablespoon oil, tie legs with twine, and nestle in center.
Roast chicken and vegetables: Roast, flipping vegetables around edges once, until chicken is golden and a thermometer inserted into thickest part of breast (avoiding bone) registers 160°F, 55 to 60 minutes.
Remove chicken and lemons: Transfer chicken and lemon halves to a carving board and tent loosely with foil.
Continue to roast vegetables: Flip vegetables; return to oven and roast until caramelized and tender, 15 to 20 minutes more.
Carve chicken and serve: Carve chicken and transfer to a platter or return to roasting pan. Sprinkle with parsley, squeeze lemon over top, and serve with vegetables.
