An ice luge, a quick Google search informs me, is an ice sculpture which is carved so that one can drink alcohol from a channel from inside or on top of it. In this case, pour liquor into the top of the Star Destroyer model. It flows over the middle and to the front, awaiting your lips. Instructables user Incrxtc made this one from a 300-lb. block of ice.
Link via Geekologie
Nothing like a bit of drunk slobber to flavor your drink.
Hopefully you meant "cup" instead of "lips".