On each users Launchpad homepage, there's a tab entitled Bugs. I've been looking through the Launchpad API reference for the person object but can't find anything that seems like it would return all the bugs associated with a particular user.
Have I just missed something or is there no easy way to use the API to do this? If that's the case, then how is Launchpad going about compiling that list?
Launchpad itself uses in-process Python APIs, not the web API. However, you can use the searchTasks() web API
lp.people['lifeless'].searchTasks()
would find all bugs related to me, for instance.