Answer: EndNote only allows one user to open a library and add and edit records at a time. EndNote does not perform "record locking" functions which allow multiple users to edit records in a shared database at one time.

You do have the option of setting the library properties as Read-Only in Windows (or Locked on a Mac), this will allow multiple people to open the library at the same time, but nobody will be able to add or edit references when the library is opened with Read-Only access.