Please go to the Catalog Settings in Lightroom, and then see the Location in the General Tab.
Click on Show, and then copy the Lightroom Folder to the external drive.
Once done, launch Lightroom by double clicking on .lrcat from the external drive.
Let me know if it helps.
You can move the catalog file to the external hard drive using your operating system to a newly created empty folder. Then double-click on it to open it.
Use Windows Explorer / Mac Finder to copy the folder containing the catalog (the default location is usually inside the Pictures or My pictures folder) to the external drive.
Now double-click the catalog file (.lrcat) in the new location to launch Lightroom,
Once you're sure that everything works ok, you can delete the Lightroom folder from your internal drive.
It's probably a good idea to move the previews folder as well. The previews need to be in the same folder as the catalog. If you don't move the previews then Lightroom will have to start all over building previews in the new location.