If you’re using bamboo or wooden skewers, soak them in water for 30 minutes. Meanwhile, start the coals or heat a gas grill for medium direct cooking. Make sure the grates are clean.
Cut the chicken into 1-inch pieces, toss with the oil, and sprinkle with salt and pepper. Alternate the chicken, sausage, and lemon on the skewers, packing the food fairly tightly. (You can assemble the skewers several hours ahead, cover, and refrigerate until ready to grill.)
Put the skewers on the grill directly over the fire. Close the lid and cook, turning the skewers several times, until the chicken and sausage are no longer pink in the center, 8 to 12 minutes total. (Nick with a small knife and peek inside.) Transfer to a platter and serve.
Adapted from How to Grill Everything, © 2018 by Mark Bittman. Reproduced by permission of Houghton Mifflin Harcourt. All rights reserved.