Eg. "Large" = 2048x2048 and I can't choose 2048x1365 (2X3 ratio)?
When using JuiceboxBuidler-Pro to create a gallery and resize images, you can set whatever image dimensions you like (in the 'Set Image Sizes' control panel after clicking the 'Change Sizes...' button on the 'Images' tab).
Please note that these image dimensions are maximum image bounds (rather than the actual dimensions for the resized images).
Images are resized respecting their aspect ratios and the resized images will always be within the maximum image bounds.
However, if your source images are square, then the resized images will also be square.
It seems that the background always be square
The background will always be the same size as the gallery itself.
The gallery dimensions are set via the galleryWidth and galleryHeight configuration options (in JuiceboxBuilder-Pro's 'Customize -> Lite' section) which are set in the embedding code.
galleryWidth and galleryHeight can be fixed pixel values or percentages.
If using a galleryWidth of 100%, for example, then the gallery's actual width will be 100% of the width of the gallery's parent container (so the gallery's actual width will be dependent on other containers and CSS on the embedding page).
I use Drupal and it is probably in the module the size is fixed (image style).
The Juicebox Module for Drupal is an unofficial plugin which was not written by ourselves.
As such, methods of resizing images and setting gallery dimensions will likely be different to how it is done in JuiceboxBuilder-Pro.
If the module's own documentation (found here) does not help, then I'd recommend that you post your query in the Drupal forum where the author of the module (Ryan Jacobs) should be able to help you further.
He is active and very helpful in the Drupal forum and has a much better knowledge that I have of both the module and Drupal itself.
I hope these notes point you in the right direction.