The archive lyx-1.4.3-cygwin.tar.gz contains an unofficial cygwin version of LyX. Here you can find both a native Qt3 GUI version of LyX (no X-server needed) and an Xforms/X11 binary which maybe preferred by Win98/ME users due to its low demanding on resources. Please take a look at the included README for instructions on installing the package. The directory cygwin-package is a repository for the official cygwin Qt3/X11 version of LyX. You don't need dowloanding the files contained in this directory (and indeed you shouldn't) in order to install the official cygwin version of LyX. Instead, you should use the setup.exe cygwin installation tool, point it to your nearest cygwin mirror and select LyX for installation.