Pat the chicken pieces dry and season all over with sea salt and freshly ground black pepper.
Heat 2 tablespoons of extra virgin olive oil in a large skillet over medium heat until shimmering.
Add the chicken to the skillet and cook until browned on the first side, about 6–8 minutes.
Turn the chicken pieces, place the thin lemon slices on top of the pieces, and continue cooking until the second side is browned and the chicken is cooked through (internal temperature 165°F/74°C), about 6–10 more minutes depending on size.
Remove the chicken and lemon slices from the pan and set aside on a plate, keeping the pan over medium heat.
Add the minced garlic to the hot pan and cook, stirring, for about 30 seconds until fragrant; sprinkle in 1 tablespoon flour and stir until the mixture is bubbly and combined.
Slowly whisk in 3/4 cup milk, then add 1 tablespoon lemon juice, chopped parsley, and 2 teaspoons fresh thyme; bring the sauce to a gentle boil while whisking.
Reduce heat to low and simmer the sauce for about 5 minutes, stirring occasionally, until slightly thickened; taste and adjust seasoning with salt and pepper if needed.
Return the browned chicken to the skillet and spoon the lemon-garlic sauce over the pieces, then serve immediately.