If you want to do this using Lightroom then you would have to use the print module to specify the dimensions of the white area. Then you print to a file. It would probably be easier to do this using Photoshop if you have a lot of it to do.
Using LRmogrify2 as a plug in for LR you can extend the canvas with an equal border on all four sides. If I understand your enquiry correctly this will achieve what you need assuming of course you start with images which are the desired dimensions and want to place them in a white bounded box to customer specification. As post-processing plug in it works well with batches, LRMogrify is a powerful tool but has a steep learning curve. Note: if you are working on a PC you have a more complicated install of a legacy version of ImageMagick.
Thank for your replies. I will try both ways…