What's the best way to fix a cracked cooler lid?

A two-part epoxy like JB Weld is the easiest and most durable fix. Clean the crack with soap and water, roughen the surface with sandpaper, mix the epoxy, press it into the crack, spread a thin layer over the top, and clamp it for 24 hours. Don’t use superglue, hot glue, or duct tape—they won’t handle the stress or temperature changes.