Get cygwin
Get cygwin from and install (at least) the following packages:

Launch then a cygwin console from the menu or the desktop. This will give a unix like environment for compiling LSE/OS. For a better comprehension of the following sections please familiar yourself with the way as Cygwin handles the Windows drives as Unix paths.

Get the elf_i386 cross compiler
Natively, the cygwin compiler and the linker (binutils) generates PE file (i386pe) which is specific to WIN32 architecture. LSE/OS uses ELF as a native file format so we need to get a elf_i386 specific compiler and binutils distribution. Simply get the package xgcc-cygwin-sos.tar.bz2 here (thanks to David Decotigny) and install it in / (the cygwin directory) then type the following commands:

$ tar xvf xgcc-cygwin-sos.tar.tar     
This will install files in /usr/local/stow
$ cd /usr/local/stow && stow binutils-2.16 && 
stow gcc-3.4.4 && stow mtools-3.9.10 
That will install the cross compiler binaries in your cygwin environment.

Get LSE/OS from Sourceforge
Type the following commands:

$ cvs login 
Type Enter at password prompt. There might be an error (.cvspass), ignore it
$ cvs -z3 
co -P lseos
If you don't have CVS you can download the last release here: here.

Get lseos.img
Note a GRUB disk is a FAT filesystem, we are going to use this image generated from a Linux box and replace files inside it (GRUB is not yet available for cygwin). Copy it in the LSE/OS root directory. Get it here: lseos.img.

The file is located in the root directory of LSE/OS.

$ sh

Type "make"
Simply type "make" in the lseos directory, it will compile and generates all the binaries and the file lseos.img in the 'conf' directory

$ make

Test the image with Qemu
Download the Qemu windows version (at least 0.8.0) here and launch the lseos.img as a floppy:

C:\Program Files\Qemu> qemu.exe -L "\Program Files\Qemu\bios" 
-m 32 -fda lseos.img