If the metadata is integrated into the main file then the main file is generally rewritten by the majority of operating systems/file systems in most computing systems used by photographers. I'm not aware of any current scenario which, even if a file system allows for the possibility of partial rewriting of files, actually occurs in such a way when using Lightroom.

If the metadata is stored in a separate sidecar file then only the sidecar file needs to be rewritten. With Lightroom the user has the option to use separate XMP sidecar files for storing metadata and the editing steps taken when working with an image file. The user also has the option to include the metadata inside the image file itself. There are advantages and disadvantages to either choice.

There are file systems that handle changes to files in a way that doesn't rewrite an entire file each time a file is changed, but they're not in very common usage by consumers who use their home computers to store photographs, or even by most professional photographers. If you use file systems such as ZFS or ReFS (that even theoretically allow for the possibility of partial rewriting of files) for storing photos you are in a very small minority.

As the number of users adopting Apple's new APFS (through upcoming hardware replacement) grows that may change over time in the future, and applications such as Lightroom might leverage such capability in the future. As of now most photographers aren't using such a file system on their computers, and even those who are don't gain anything with regard to partial file writing if the application, such as Lightroom, doesn't use the capability.