As far as I've been able to tell, their hosting service generated online viewers and embeds server-side, rather than their desktop software generating it and uploading it to pictures.lytro, Facebook, or 500px (the supporting services). It won't even let you do that kind of export without logging into api.lytro.com first. (Their Desktop 5 software is a .NET app if anyone wants to try poking at it.)
After their hosting service shut down last year, I crawled every embed the Internet Archive had, and downloaded the additional JSON and JPEG assets necessary to restore the embeds. https://www.archiveteam.org/index.php?title=Lytro
Those were eventually added, so now any embeds the Wayback had before the shutdown should work again, e.g. http://www.theverge.com/2014/7/30/5949913/lytro-illum-review v. https://web.archive.org/web/20170317183900/http://www.thever...
It's unclear whether all the Lytro file formats (including their later standard "XRAW") have any sort of documentation. The earlier formats (from their pre-Illum camera) do, e.g. https://github.com/nrpatel/lfptools but not the later formats, which include camera calibration data.
The viewers on GitHub, e.g. https://github.com/damienfir/lytrogl and https://github.com/behnam/php-lytro are only for their earlier formats.