I'm sorry to hear about this.
All the information for WP-Juicebox galleries is stored in wp-content/uploads/juicebox/ (one XML file per gallery, e.g. 1.xml for Gallery #1, 2.xml for Gallery #2, etc.). The 'Manage Galleries' page reads this folder to see what XML files are present and then displays the results in a table.
Ordinarily, the only way for all this data to disappear would be to click the 'Delete All Data' button on the Manage Galleries page (and then click the 'Are you sure?' button).
All the images for WP-Juicebox galleries are stored in WordPress's own Media Library (for local galleries) or on Flickr's servers (for Flickr galleries). There is no separate store of images for WP-Juicebox galleries. Just for reference, 'Manage Galleries -> Delete All Data' does not delete any images (just the gallery data (XML files) in wp-content/uploads/juicebox/ and the plugin preferences in the WordPress database). After 'Delete All Data' all gallery images remain either in the Media Library (attached to their respective posts) or on Flickr's servers.
The first thing to do is check to see if there are any XML files within wp-content/uploads/juicebox/.
Perhaps your web host has a backup of your site which can be reinstated. This would be worth investigating.
I hope this points you in the right direction.
Please let me know how you get on. Thank you.