In a large, non-reactive bowl, combine the vinegar, sugar, kosher salt, bay leaves, and thyme and stir to dissolve the sugar and salt. Place the chicken in the bowl with the vinegar mixture. Add enough cold water to cover the chicken, cover and refrigerate overnight or until ready to use.
Preheat the oven to 350°F.
Rinse the chicken and pat dry. Place on a rimmed baking sheet, skin-side down. Drizzle the chicken with the olive oil and lemon juice and season with salt and pepper. Place in the oven to roast for 30 minutes.
While the chicken is roasting, Preheat a gas grill to medium-low, or start a fire in a charcoal grill and let the coals burn to medium-low, a gray color with a slight glow. (You should be able to hold you hand over the flame 5 to 6 seconds when the coals get to this point.)
Remove the chicken from the oven and brush with barbeque sauce. Place the chicken on the grill grates, skin-side down. Baste the bone-side with the barbeque sauce. Cook the chicken, skin-side down, for about 5 minutes, checking often to make sure the fire is not too hot. The skin should be crispy and slightly charred.
Turn the chicken over and baste with the barbeque sauce and sprinkle with the herbs. Continue to cook 5 minutes more to crisp the other side. Move the chicken from the direct coals, baste with the sauce again, and close the lid to the grill. Continue to cook for another 12 to 15 minutes, until the internal temperature at the thickest portion of the thigh is 165?F. Remove from the fire, and let rest for 5 minutes. Serve warm with additional barbeque sauce if desired.
Sweet & Spicy BBQ Sauce
In a large saucepan over medium heat, heat the olive oil. Add the onion and cook and stir for about 5 minutes, until soft and golden. Add the garlic and cook and stir for 1 minute more. Pour in the ketchup and coffee, stirring to mix. Add the chili sauce, vinegar, Worcestershire sauce, sugar, mustard, red pepper flakes, salt, and black pepper and stir to mix. Squeeze the lemon juice into the sauce, add the squeezed halves, and stir.
Bring the sauce to a low boil, reduce the heat to a simmer, and cook for about 30 minutes, stirring occasionally, until the sauce thickens and reduces slightly. Remove from the heat, let cool slightly, and remove and discard the lemon halves. Refrigerate in an airtight container until ready to use, or for up to 3 weeks.