To expand a bit more on Private Bugs.
There are two major types of private bugs:
(this is centered on Ubuntu, but should be similar on other projects, like Lubuntu)
- born private
- made private later on.
For the born-private: these are usually security issues, or Apport crashdump bugs. The apport crashdumps are born private because they carry a coredump file -- and it can carry a LOT of private data in it. Additionally, apport processing runs a GDB 'bt full' for both the offending thread (the one that got hit) and for all threads. The 'bt full' sports variable assignment values. Depending on the program, and where it got hit, these variables values could also hold private data. No matter what, at the end of apport processing, the coredump is deleted.
So... apport will, usually, not make a crashdump bug public. But it knows about it, and will match as needed, marking newer bugs as duplicates.
A subset of Launchpad users have access to these bugs, and can manually review and decide on an action -- the worst scenario is we see private data, and will have to discuss with someone else (a maintainer/developer of the package) if the private data is critical; if it is not, we can edit/remove the offending pieces, and make the bug public. If the "offending" data is private, on the other hand, there is not much we can do. But these are very unusual cases, I do not remember seeing one myself.
So, to summarise: yes, your bug can be dupped to a private bug. In this case, please pop in #ubuntu-bugs, or email Bug Control/Ubuntu-QA, and ask for someone to perform the check. We will be happy to help.