Is there anyone running his/her own instance of Launchpad?
Solution 1:
According to the FAQ:
"Launchpad's production configuration information and some configuration-specific admin scripts are not part of the Launchpad code base..."
...so you would need to create these files yourself or remove the functionality that depends on these scripts. Based on the contents of that paragraph, I get the impression that these files are not trivial and contribute some pretty major functionality to Launchpad.
And it doesn't end there. Since Launchpad is an extremely active project, updates to the codebase are very frequent and could break your private instance very easily. The FAQ states:
"Essentially, there's a risk of a private instance becoming an unintentional fork, where its code cannot be safely updated due to the data in the local instance being incompatible with the latest database schema or code assumptions."
So you would have to stay up to date on all of the latest patches and changes and also make sure that they integrate with your instance without any problems.
According to the FAQ, the purpose of releasing the source code for Launchpad was not so that others could run "Launchpad-clones," but so that anyone can help contribute patches / bugfixes for the original instance of Launchpad.
All of this is to explain why there are no other instances of Launchpad anywhere. It's simply too much work and for very little gain.
Solution 2:
I know of one instance of Launchpad other than launchpad.net. It lives at: https://quickbuild.pearsoncomputing.net/. I believe it was setup mostly to take advantage of the build system in Launchpad.
There have been a few attempts to get LP running and people often ask questions on IRC about how to run a Launchpad themselves. However, as far as I know, the URL for QuickBuild above is the only person to have some success at this.