Remove giblets and liver from chicken's cavity; discard or reserve for another use. Rinse chicken thoroughly under cold water, inside and out, then pat dry, making sure the cavity is as dry as possible. Season cavity with salt and pepper, then stuff with lemon, rosemary, and garlic. Truss chicken or tie legs together with twine. Rub skin with 2 tablespoons of butter. Season all over generously with salt and pepper.
Place chicken in a small roasting pan fitted with a rack or a large ovenproof skillet. Roast with legs facing toward the rear of the oven until an instant-read thermometer inserted into the thickest part of thigh registers 165 degrees, 50 to 55 minutes.
Remove twine and transfer chicken to a platter, let rest 10 minutes.
Spoon and discard fat from juices in pan.
Place pan over medium-high heat. Pour in wine or stock to deglaze pan, stirring and scraping up browned bits with a wooden spoon.
Cook until reduced by half; add butter, swirling pan until melted and incorporated.
Remove from stove and pour sauce through a fine mesh sieve into a small saucepan. Season with salt, if necessary.