I would like to find out if there is wiki software that runs on SQLite.
Sure is.
Instiki (What Is Instiki) is a basic Wiki clone so pretty and easy to set up, you’ll wonder if it’s really a wiki. Runs on Rails and focuses on portability and stability. Supports file uploads, PDF export, RSS, multiple users and password protection. Some use Instiki as a CMS - Content Management System because of its ability to export static pages.
According to the SQLite Users Page, the CVSTrac program is using SQLite as its internal database structure (you have to follow the link to the CVSTrac site to see the details). I'm sure there are others by hunting around the site.
Any of the Django ones should be able to, because Django is flexible about which Database backend it uses and SQLite is one of the options.
Fossil, which is a DVCS with many other features (including a wiki) is built on top of Sqlite (in face, made by D. Richard Hipp who wrote Sqlite ). It can be found at: http://www.fossil-scm.org/index.html/doc/tip/www/index.wiki