I don't know how a seperation would work in this particular instance, but in Australia it would typically be achieved by a distribution in specie, resulting in each shareholder retaining the same % ownership interest in two seperate companies. No doubt there will be a raft of tax, accounting, legal, governance and NYSE listing issues to work through, which will take time.

I can't see why LAC would go through the pain of doing this just to secure a (let's say) $200m DOE loan. I reckon the available loan amount might be much much larger - >> $500m?. That would certainly be worth it, I would say.