Place on a rimmed platter, shingling slices.
Pull chicken meat from bones and slice ½' thick. Transfer to a cutting board and let rest 10–15 minutes. If desired, uncover grill, move chicken over to hotter side, and lightly char a minute or two. Turn chicken over, cover, and continue to grill until an instant-read thermometer inserted into the thickest part of breasts registers 160°, 8–10 minutes longer. Grill chicken on cooler side of grill, skin side down, until skin is browned and starting to crisp, 15–20 minutes. Grill oiled lemon slices over hot side of grill, turning once, until charred in spots, about 3 minutes. Pat chicken dry again (the salt will have drawn out more moisture) and rub with 2 Tbsp. Slice remaining lemon in half and squeeze juice into another small bowl (you should have about ¼ cup). Set remaining lemon slices aside for serving. oil and toss to coat season with salt and pepper. Place half of lemon slices in a small bowl.
Thinly slice 1 lemon crosswise into rounds pluck out seeds. Place on a rimmed baking sheet let sit at room temperature at least 30 minutes and up to 1 hour. Pat chicken breasts dry season generously all over with salt and pepper. Prepare a grill for 2-zone heat (for a gas grill, set one burner to medium-high and one or two burners to low for a charcoal grill, bank most of the coals on one side).
