The bundle installer installs MiKTeX and LyX, then launches the configuration script, which looks for various MiKTeX packages (quite a few of them, actually) by running tiny LaTeX jobs that require them. The default behavior for MiKTeX's package manager (mpm.exe) when LaTeX requires a package not currently installed is to go off to the Internet and download the package. Given the number of packages sought by the configuration script, this can take a considerable amount of time, during which the installer looks as if it's stuck (it's not -- it's just waiting for the configuration script to complete). If you don't have a live Internet connection, I think mpm will wait indefinitely for one (in which case the installer really is stuck).
You can use the MiKTeX settings application to change the reaction to missing packages to either of two other choices: prompt you each time it wants one (you'll know the process is working but you'll be nagged to death for permissions); or don't look for the missing package and just fail silently. My suggestion is to pick one of these and then run the configuration script again (Tools > Reconfigure, assuming LyX will start). If you pick the "just say no" option, you can always install missing packages later, although you may have to reconfigure LyX after installing them. If the problem was that you did not have an Internet connection, I think you can also turn one on, rerun the installer and watch the Lord of the Rings trilogy back-to-back-to-back while the installer runs. Paul
