Log into en.gamigo.com with an account you play LC US with. Go to My Gamigo.
On the right side of the screen you will see "More Games". Find Last Chaos Europe in the list and click it.
It will now be a banner under the main part of the page. Click "Play now" and it will open a popup window asking for game username and password.
Fill those out, and your account is now linked to an EU account. You can now download any EU version and play on it with the login details you input into the popup.
When you have an Eu version downloaded, go into Drive C > gamigo and rename LC US folder to "LCUSA". Go into add/remove programs and uninstall Last Chaos.
Now you are free to install any other version you have downloaded and still be able to play your LC US normally.