Fridge Brilliance: The Tree of Life represents a human body. The Regi trio and the orange blobs are the tree having an allergic reaction to Ash and co., and it goes into anaphylactic shock. Ash and Lucario using their auras is emergency treatment, followed by Mew's later treatment. The entire thing is a metaphor.
Fridge Logic: Wouldn't HALVING both Ash and Lucario's auras (probably requiring a week or two of bedrest for the two afterwards) have been better than Lucario pushing Ash out of the way, using up all of his aura, and dying from it as a result?
Maybe Lucario thinks that Ash hasn't developed his aura ability enough to be of much help, and the only thing letting him try would do is draining all of his energy, possibly killing him. Since Ash is so much like his master, he might not have wanted to risk it. Or he actually wanted to die, to be with Aaron again.
Pretty sure that anybody involved in the aura "ritual" would die regardless of how many were involved. Even if the power was divided like that it probably wouldn't make much difference for only two of them. Either way, it certainly seems as though both Ash and Lucario were going to die from that if they'd continued together.