Not sure I'm properly visualizing the arrangement you're going for, but I think Lightroom can do this.
The goal is to efficiently fit multiple images in as small a (paper size) space as possible. Maybe rotation is allowed (allows optimal fitting), maybe not, maybe some edge-space must be left between images, maybe not.
One solution is to work with a template, like Mark suggested. The drawback is that it's not flexible, and one always has to fill the template in the same way with the same image sizes. Switching/deleting images or removing one, will require lots of editing if multiple sizes are involved.
The other solution is to automate the process, e.g. with a custom made Photoshop script (which is Javascript like, so it can be quite flexible, but requires maintenance for newer versions).
The easiest solution is using an existing program that does the nesting automatically (and creates higher quality output).
Cheers,
Bart