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Preheat oven to 425°F. Pat chicken dry with paper towels; sprinkle with ½ teaspoon salt.
Heat oil in a large ovenproof skillet over medium-high heat. Add the chicken; cook, undisturbed, until golden brown on the bottom, 4 to 5 minutes. Flip the chicken and arrange lemon slices around the chicken in the bottom of the pan. Sprinkle with thyme and rosemary.
Transfer to the oven; roast until an instant-read thermometer inserted into the thickest part registers 165°F, about 8 minutes. Transfer the chicken and lemon slices to a cutting board; let rest for 5 minutes. Do not wipe the pan clean.
Heat lemon juice, pepper and the remaining ⅛ teaspoon salt in the pan over low heat. Whisk in butter, 1 piece at a time, until melted and a sauce forms, about 45 seconds to 1 minute. Remove from heat and stir in tarragon. Slice the chicken breasts in half; serve drizzled with the sauce.