Regarding administrative rights, I'm surprised the obvious solution has
not been aired:
When the installer is started without administrative rights, warn the
user that the bundled Python and Miktex only install with administrative
rights. Explain the consequences of this: PDF and Postscript export will
not available, but the user is free to install and able to use LyX anyway.
If administrative rights become available at some point, rerun the
installer, and it will install Miktex and Python correctly, and the
system will work.
This requires some hours of development and testing, which are probably
not available.
Regards,
Asger