I then referenced the library by adding the dll file by "Add Project Reference".
You created a specific file reference. The class library contains other library dependencies that the main application knows nothing about because the dependent DLLs are in the class library's bin folder.
Assuming both projects are part of the same solution, create a project reference rather than referencing the DLL directly (file reference). Otherwise, you'll need to physically copy the dependent DLLs or make a reference to the missing libraries in the main project both of which can cause headaches down the road.
Reference documentation.
Manage references in a project