That's a really practical question! From my experience, the answer is: it depends, but often not directly interchangeable. Most city-issued or standard public space trash cans use specific models from particular manufacturers. While lids within the *same model and brand* are perfectly interchangeable, a lid from a different brand or style rarely fits correctly due to variations in size, hinge mechanism, and locking tabs.
If a lid on a public bin breaks, it's best to report it to your local public works or sanitation department. They have the specifications and can order the exact replacement part. For a personal outdoor bin, check the manufacturer's label (often on the underside of the rim or the bin itself) for a model number. Contacting the manufacturer or a parts supplier with that number is your best bet.
Some cities are moving toward more standardized bins to simplify maintenance. In those cases, interchangeability within the same size class (e.g., 60-gallon wheeled carts) is higher. However, assuming lids are universally swappable can lead to a wobbly, ill-fitting lid that doesn't contain odors or deter pests. Your safest path is to seek an exact match.