Create a normal FAT32 partition and install your WinME as usual. After WinME is up and running, create the setup bootdisks for RedHat 6.2. Boot with that bookdisk and you should be able to enter the RH installation. During the setup, use fdisk and create a Linux Native partition (which is where you will install RH), and a Linux Swap partition for you swapfile in Linux. Continue the installation process and when you setup LILO, the option to boot into the windows FAT32 partition should be avaliable. Remember to install LILO on the MBR of your drive.
Once the installation is finished, you will have the option to type in commands at the LILO prompt to boot into either OS. It is not hard to do, quite straightforward... Good Luck!