One example is if you use unsynchronized interior mutability. For example both Cell and RefCell implement Send but not Sync because it is fine to send one to another thread, because that thread now owns it and it no one else can access it. But it is not fine to share it because Cell and RefCell use interior mutability without synchronizing access. So if two different threads tried to access either of them there would be a data race.
Another case is if you are using trait objects.
Box<dyn Trait>: !Send + !Sync
Box<dyn Trait + Send>: Send + !Sync
Box<dyn Trait + Send + Sync>: Send + Sync
Box<dyn Trait + Sync>: !Send + Sync
The reason for this is because if you don't mark the trait object Send or Sync you can put types inside that are not Send or Sync.
It looks like DirectoryLock is only Send because of the Box<Drop + Send + 'static> inside of it (from looking at the source code).