Pat chicken breasts dry; season generously with salt and pepper. Place on a rimmed baking sheet lined with parchment paper; let sit at room temperature at least 30 minutes and up to 1 hour.
Prepare a grill by lightly oiling the grate.
Slice 1 lemon in half and squeeze juice into a small bowl. (You should have about 1/4 cup.) Set aside.
Thinly slice the second lemon crosswise into rounds; pluck out seeds. Set half of these slices aside for serving.
Place remaining lemon slices in a small bowl. Add garlic and 1 tablespoon olive oil and toss to coat; season with salt and pepper. Grill oiled lemon slices over hot side of grill, turning once, until charred in spots, about 3 minutes. Transfer to a plate.
Pat chicken dry again (the salt will have drawn out more moisture) and rub with 2 tablespoons olive oil. Grill chicken on cooler side of grill, skin side down, until skin is browned and starting to crisp, 15–20 minutes. Turn chicken over, cover, and continue to grill until cooked through. If desired, uncover grill, move chicken over to hotter side, and lightly char a minute or two. Transfer to a cutting board and let rest 10–15 minutes.
Pull chicken meat from bones and slice ½-inch thick. Place on a rimmed platter, shingling slices. Scatter thyme sprigs, olives, grilled lemon slices, and reserved fresh lemon slices over. Season with more salt and pepper; drizzle reserved lemon juice and remaining 1/2 cup oil over. Let sit at least 15 minutes and up to 1 hour before serving.