Preheat grill on medium and spray grates with non-stick oil.
Trim and pat chicken breasts dry; season generously all over with salt and pepper. Place on a rimmed baking sheet lined with foil or parchment (for easier clean up); let sit at room temperature at least 30 minutes and up to 1 hour.
While chicken is sitting, thinly slice 1 lemon crosswise into rounds; pluck out seeds. Place lemon slices in a small bowl. Add crushed garlic cloves and 1 Tbsp. oil and toss to coat; season with salt and pepper. Juice remaining lemon (you should have nearly ¼ cup). Tear or cut olives in half. Set lemon juice and olives aside.
Grill lemon slices (and smashed garlic cloves) turning once, until charred in spots, about 3 minutes total. Set aside.
Pat chicken dry again (the salt will have drawn out more moisture).
Grill chicken skin side up, 15–20 minutes covered. Turn chicken over (skin side down), cover, and continue to grill for 8-10 minutes. If using an instant-read thermometer, it should register 160° when inserted into the thickest part of the breasts. Transfer chicken to a cutting board and let rest 10–15 minutes.
Using your hands, pull chicken meat from bones and slice into ½” thick pieces as I did in above photo.
Place chicken on a rimmed platter, fanning slices. Scatter thyme sprigs, olives, and grilled lemon slices over the chicken. Season with more salt and pepper. Drizzle reserved lemon juice and remaining ½ cup oil over. Let sit at least 15 minutes and up to 1 hour before serving.