Microwave capers and ½ cup olive oil in bowl (capers should be mostly submerged) until capers are darkened in color and have shrunk, about 5 minutes, stirring halfway through. Using slotted spoon, transfer capers to paper towel-lined plate (they will continue to crisp as they cool); set aside and reserve oil. 

Combine caper oil, squash, tomatoes, 1 teaspoon salt, and 1 teaspoon pepper in bowl. Arrange four 18 by 14-inch sheets aluminum foil flat on counter. Divide vegetable mixture evenly among foil sheets. Pat cod dry with paper towels and sprinkle with ¼ teaspoon salt and ¼ teaspoon pepper, place on top of vegetables, then top with lemon slices. Bring short sides of foil together and crimp tightly to seal. Crimp remaining open ends of packets. 

Grill packets over hot fire (covered if using gas) until cod registers 135 degrees and vegetables are tender, about 10 minutes (insert an instant-read thermometer through the foil into thickest part of fish to test for doneness). Carefully open packets, allowing steam to escape away from you. Using thin metal spatula, gently slide cod, vegetables, and any accumulated juices onto individual plates. Drizzle with olive oil to taste and sprinkle with crispy capers. Serve.