In a saucepan over medium heat, combine the ketchup, soy sauce, honey, mustard, sugar, garlic, and lemon juice. Bring to a simmer and cook until thickened, about 10 minutes. Set aside to cool.
Set up a grill or a grill pan. Remove the skin and cut the pineapple into 1 1/2-inch chunks. Thread the chicken and pineapple pieces onto skewers, alternating between them. Brush them with olive oil and sprinkle with salt and pepper before grilling. Remove the garlic cloves from the sauce and discard; reserve half of the sauce in a bowl for later.
Brush the skewers with some of the sauce. Grill them for 10 to 15 minutes, basting them frequently with the barbecue sauce, until they’re done through. Serve with extra BBQ sauce on the side for dipping.
