You can store full size copies of all your files locally in Lightroom Desktop (AKA Lightroom CC). On PC go to Edit>Preferences, on Mac, Lightroom>Preferences, and click on the Local Storage tab. Choose the option to store a copy of all files locally and specify where you'd like to store them. Note that these are copies of your originals - they are not JPEG previews or DNG smart previews.
Whoops, I almost forgot - you'll also see an option to store smart previews locally, if you wish to save a lot of space and don't need the actual originals. These aren't full size though - they are limited to 2560 pixels.
Finally, you can also right-click on an album and choose Store Album Locally to store those originals locally.