Place chicken on a large plate and season generously with salt and pepper; cover with plastic wrap and refrigerate overnight. 

Preheat oven to 450 degrees. 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 in a large roasting pan, with shallots in center and carrots, potatoes, and lemon toward edges.

Rub chicken with remaining 1 tablespoon oil, tie legs with twine, and nestle in center. Roast, flipping vegetables around edges once, until chicken is golden and a thermometer inserted into thickest part of breast (avoiding bone) registers 160 degrees, 55 to 60 minutes. Transfer chicken and lemon halves to a carving board and tent loosely with foil. Flip vegetables; return to oven and roast until caramelized and tender, 15 to 20 minutes more. Carve chicken and transfer to a platter or return to roasting pan. Sprinkle with parsley, squeeze lemon over top, and serve with vegetables.

Place chicken on a large plate and season generously with salt and pepper; cover with plastic wrap and refrigerate overnight. 

Preheat oven to 450 degrees. 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 in a large roasting pan, with shallots in center and carrots, potatoes, and lemon toward edges.

Rub chicken with remaining 1 tablespoon oil, tie legs with twine, and nestle in center. Roast, flipping vegetables around edges once, until chicken is golden and a thermometer inserted into thickest part of breast (avoiding bone) registers 160 degrees, 55 to 60 minutes. Transfer chicken and lemon halves to a carving board and tent loosely with foil. Flip vegetables; return to oven and roast until caramelized and tender, 15 to 20 minutes more. Carve chicken and transfer to a platter or return to roasting pan. Sprinkle with parsley, squeeze lemon over top, and serve with vegetables.