Cut in half and grabbed something? laughable. IF you lived through that you would be in shock and unable to do anything. PERIOD
Windu was not dead or even unconcious as he flew out the window, the fall killed him and thats that. Force lightning didn't kill luke or knock him out.
Gotta love the way people pull EU stuff to prove a point. Its retconn fan fiction that just messes with movie cannon.
No the lighting killed him, he was blasting Mace Windu with full power with Luke he was just torturing him. To reiterate
Defenseless, Windu was bombarded with Sith lightning as Sidious unleashed a torrent of deadly energy at the Jedi Master. The forked bolts of lightning penetrated Mace's body, illuminating his form from within. The final blast bodily lifted him into the air, sending his form hurling into the Coruscant skies, to crash lifelessly somewhere in the vast cityscape below.