I don't think Jesus died thinking a false thing about God.
Jesus knew that sin separates and is the cause of death.
Mercy triumphs over death.
To triumph over death you must have a death.
Jesus was obedient even unto death.
I think he was quoting scripture to reveal that God was answering David's call for deliverance and fulfilling the prophets.
Jesus did die, but not believing lies. In Romans 6 we see that of Christ's physical death was a LIKENESS to our death to sin. Jesus died and was resurrected to save US from believing lies, not himself. That's what makes his crucifixion selfless.
Christ was the spotless lamb not a believer of untruths about his father. The two were one on the cross.
I believe Jesus was being truthful when he said "Elí, Elí, lemá sabachtháni?
He was not saying it for effect.
How could Jesus die( Mystery?)one.