User blog comment:IamJakuhoRaikoben/Chapter 386: Galaxia Blade, Review./@comment-7418318-20140530085923

Apart from the three possibilities you already mentioned, why Lucy is so drained, I think there's a fourth.

Lucy summoned the Spirit King, so it's possible (even likely I'd say) that she is sustaining him like the other Spirits. Apart from being logical, this theory is also supported by this chapter. Just when Lucy falls over from exhaustion, Mard suddenly comments about the King weakening and ol' mustache-man goes for a final attack before vanishing.