The software underlying the nLab is a heavily modified fork of Instiki. The code is moving further and further away from the original Instiki, and the plan (hopefully by the end of 2019) is to have evolved to what is essentially an entirely distinct codebase, no longer a fork.
The nLab is currently not well suited to developing locally. This will change with the move to a distinct codebase. If you are interested in working on something, get in touch with Richard Williamson, who will be happy to suggest tasks or provide suggestions for how to work locally on something.
All help is very welcome! Just get in touch on the nForum to express your interest, and we'll take it from there.
The original Instiki is licensed under the same license as Ruby. All code which is written by Richard Williamson, for example all code under script/src, is made available without any restriction whatsoever, except that this unrestricted availability is not permitted to be superseded: anybody is free to use, license, or refer to the code however they wish, except that it is not permitted to supersede the unrestricted availability of the original code referred to herewith.