That's not Cube. In MtG terms, Cube Draft is made with a predetermined set of cards, that get shuffled and divided into "booster packs", yeah. But thing is, and every player is aware of that, there is only ONE copy of each card (and some cards won't make the boosters, since the Cube usually have some excess cards so even though players know the Cube, they don't know exactly what they'll see), and they are only the best crds in the game. So, the last Cube Draft MtG held, at the Invitational, sponsore Black Lotus, the moxen, Vindicate, Force of Will, Tolarian Academy, Vampiric Tutor, Demonic Tutor, Ancestral Recall, etc.
In LotR, it'd probably be the best versions of the companions, the best weapons, etc. But only one of each. I think it might be doable, and it might even turn out to be a fun format!