For the butter:
In a bowl, add butter, tarragon, sage, thyme, garlic, and lemon juice. Season with salt and pepper. Stir with a fork until all ingredients are well combined.
Transfer butter onto a large piece of wax or parchment paper and shape into a log. Wrap tightly. Make sure you seal the ends.
For the seasoning:
Grind garlic, sea salt, and pepper in a mortar. Set aside.
For the chicken:
Preheat oven to 375°F. Pat dry the chicken.
Sprinkle main cavity of chicken with kosher salt and pepper. Slide fingers under skin of the breast and upper part of legs, loosening skin. Spread seasoning mixture and lemon and herb butter under the skin. Sprinkle chicken again with kosher salt and pepper. Insert the halved lemon into the chicken cavity.
Truss the chicken and place chicken on rack in large roasting pan. Roast chicken uncovered for 1 1/2 hours.