Short answer: usually, yes—if the lid is designed as a separate, replaceable part. Many urban trash cans are modular, so you can order a new lid or hinge assembly from the manufacturer instead of replacing the entire bin. For metal bins, a broken hinge can sometimes be re-welded, riveted, or bolted; for plastic bins, a cracked lid may be replaceable if the mounting points are still solid.
That said, it is not always worth repairing. I would check four things: whether replacement lids are still available, whether the hinge mounts and body are intact, whether the repair will look and function safely in public, and whether the total repair cost is sensible compared with a new bin. If the lid is molded into the body, the hinge area is badly rusted or torn, the bin is structurally damaged, or matching parts are unavailable, replacing the whole unit is usually the better call.
For a city or facility, also consider downtime, vandalism risk, warranty terms, and consistency of street furniture. A repair is often the greener and cheaper option when the body is sound and parts are in stock. As a practical rule, repair the lid if it is a simple hinge or replacement-lid job; replace the whole bin if the repair is complex, unsafe, or costs more than about half the price of a new unit. Start by sending the manufacturer or supplier a photo of the damage and the bin model number—they can usually tell you quickly whether a lid-only repair is available.