Wash summer squash thoroughly under cold running water, rinsing any soil or other debris away.
Place squash on a clean chopping block or cutting surface. Slice the squash crosswise into circles, each about 1/2-inch thick, leaving the skin intact. Discard the stem and tip, keeping only the fleshy parts of the squash.
Sprinkle a light layer of lemon pepper on each side of the squash circles. Set them aside on a clean plate.
Coat the grill cooking grate with a light layer of vegetable oil grilling spray.
Set up the gas or charcoal grill for direct grilling and ignite the grill. If using a gas grill, this means selecting the appropriate burner (see your grill's manual). If using a charcoal grill, this means spreading coals into an even layer under the grate.
Close the grill lid and allow the grill to heat to about 350 F.
Open the grill lid and place the squash circles on the cooking grate directly above the heat source. Leave about 1/2 inch of space between each piece so heat can get between the sections and cook the squash evenly.
Grill the squash until it is just tender and slightly browned, about eight minutes on each side. Carefully turn the squash with the long-handled tongs so pieces don't tear off or slip between the grill grates into the flames.