My mother would combine everything into a pot and the sauce would just sit and simmer on the stove forever. I remember the smell would be somewhat acrid at first, like vinegar. Then the ginger, spices and lemon would take over and create this wonderful aroma. Doused on chicken and cooked in the oven, this sauce was amazing hot and cold leftover!
In a medium saucepan or a large high-sided saute pan, combine the ketchup, cider vinegar, Worcestershire sauce, soy sauce, light brown sugar, dark brown sugar, dry mustard, Dijon mustard and chili powder. Whisk to blend. Bring to a simmer over medium heat. Add the ginger, garlic and lemon slices and stir to combine. Simmer until the vinegar mellows slightly and the flavors start to meld together, about 20 to 25 minutes. Remove from the heat and allow to cool. Discard the ginger pieces.
Preheat the oven to 350 degrees F. Position the rack in the lower third of the oven. Line a baking sheet (or, if needed, 2 baking sheets) with foil. Season the chicken parts on both sides with salt, to taste. Pour about 1 1/2 cups of the barbeque sauce into a large bowl. Reserve the remaining sauce on the side. Submerge the chicken pieces in the sauce and arrange them on the prepared baking sheet with some of the lemon slices. The chicken should all be in a single layer with a little space between them. If additional space is needed, use the second baking sheet. Brush with barbeque sauce.
Put the baking sheet(s) in the oven and bake, undisturbed, for 20 minutes. Remove the chicken from the oven and use a pair of metal tings to turn the pieces to the other side. Use a pastry brush to coat the second side of the chicken with the barbeque sauce from the bowl. Do not reuse that bowl or brush again. Return the sheet(s) to the oven and cook for an additional 15 to 20 minutes. Poke a thigh with the tip of a small knife and verify the chicken juices run "clear" and not pink. Turn the broiler on and broil for a minute until the chicken is charred on top.
Warm the reserved barbeque sauce in a small saucepan over low heat. Pour into a serving bowl.
Transfer the chicken to a serving platter and serve immediately with the warm sauce on the side.