Heat oven to 350°F. In a small bowl, mash lemon zest, garlic, thyme, 2 Tbsp butter, and 1/2 tsp each salt and pepper until combined. With fingers, gently separate skin from breast and thighs of chicken. Place butter mixture under skin and spread evenly. Tie drumsticks together and tuck wings behind breast. Place chicken on a rack fitted into a medium roasting pan. Melt remaining 2 Tbsp butter and brush all over chicken, then sprinkle with 1/2 tsp each salt and pepper. Pour 1/4 cup water into bottom of roasting pan. Roast chicken 50 minutes. Reset oven to 425°F; continue to roast chicken, checking to make sure water has not completely evaporated (add another 1/4 cup if necessary), until an instant-read thermometer inserted into thickest part of thigh registers 165°F, 15 to 20 minutes. Let chicken rest at least 15 minutes before carving.