Here are a few tips to kill the demi-lich.

Use your best fighter with a +5 or bette weapon.

Hide the rest of your party. The best way i found was have the rest of them try to leave the level. They will cram themselves into the doorway and just sit there, out of sight.

Activate the lich and have your fighter kill him.

as soon as the demi-lich starts to appear, cast protection from evil on your fighter and invisiblity on the rest of your party.

Its all over for poor mr Demi-lich now. The protection spell makes your fighter invisiable to the lich and you can beat him to your hearts content.

What ever you do, DO NOT cast the protection from evil when fighting the normal Lich. YOU WILL NOT BE ABLE TO KILL HIM IF YOU DO. Not sure if its a bug or what but I've hammered on the lich for at least a half an hour and could not get him below near death when I had the pfud spell going.

Hope this helps.