You can move files across devices directly inside Lightroom.
Simply use drag & drop in the Folders pane in the Library module.
Using your computer's file manger (Windows File Explorer, Mac Finder) copy the folder tree of your desired pictures to the new drive.
It is best to do the actual file move/copy outside of Lightroom because Lightroom does not always get it right when moving large numbers of files. When it goes wrong, the files are often lost forever.
In Lightroom, using the Folders panel in the Library, right-click on the top-most folder you copied, select "update folder location" (or similar menu item), navigate to the folder on the new drive.