can I update my 3rd generation apple tv on my mac

You can update the Apple TV (3rd generation) on the device itself. How to update your Apple TV - Apple Support

The current version system software is v7.5, since 2020-03-24. Higher versions of the Apple TV software are not compatible with this model.

You can “restore” the system software through a Mac. This should only be needed if operation through the menu on the device is not available. Restore your Apple TV - Apple Support

No, you need to use a Internet connection on the Apple TV. What version of TV OS is currently installed on it?