In your question, I suspect that you were actually referring to Dr. George Lamsa and his translation, "Holy Bible from The Ancient Eastern Texts: Aramaic Of The Peshitta" from 1933. Here is his translation of Matthew 27:46:

Matthew 27:46 (Lamsa)

 And about the ninth hour, Jesus cried out with a loud voice and said, Eli, Eli, lmana shabachthani! which means, My God, my God, for this I was kept!

Dr. Lamsa was an expert in the Aramaic language and as such qualified to handle this very difficult Aramaic expression that was left in the English. There are only a few places in the English New Testament where the Aramaic words were transliterated directly into the English and then followed by the English translation of those words. This seems to imply that perhaps the translators were not totally sure on how to handle the translation of those words.

The doctrinal difference that rises out of this translation is quite stark. The widely accepted translation is as follows:

Matthew 27:46 (KJV)

And about the ninth hour Jesus cried with a loud voice, saying, Eli, Eli, lama sabachthani? that is to say, My God, my God, why hast thou forsaken me?

The generally accepted view is that when Jesus was on the cross, he became sin and at that moment God forsook him. Some have commented that the reason was that God could not tolerate sin (though there are various nuances of this thinking). The following prophesy from the Book of Psalms refers to this statement as well:

Psalm 22:1

My God, my God, why hast thou forsaken me? why art thou so far from helping me, and from the words of my roaring?

Notably, this Psalm also contains several other prophecies concerning the coming of the Lord Jesus Christ.

The Lamsa translation, on the other hand, seems to align more accurately with what the Lord Jesus Christ stated himself while he was with his disciples. Here are some relevant scriptures:

John 16:32

Behold, the hour cometh, yea, is now come, that ye shall be scattered, every man to his own, and shall leave me alone: and yet I am not alone, because the Father is with me.

Matthew 26:53

Thinkest thou that I cannot now pray to my Father, and he shall presently give me more than twelve legions of angels?

John 8:28, 29

Then said Jesus unto them, When ye have lifted up the Son of man, then shall ye know that I am he, and that I do nothing of myself; but as my Father hath taught me, I speak these things.

And he that sent me is with me: the Father hath not left me alone; for I do always those things that please him.

There is no doubt that all that Jesus Christ did was according to God's will and this would also include his dying on the cross. Jesus was also very clear in his statements that he would never be left alone by his Father. In fact he said that God would always be with him. Furthermore, it was God who made Jesus sin for man.

2 Corinthians 5:21

For he [referring to God] hath made him [Jesus Christ] to be sin for us, who knew no sin; that we might be made the righteousness of God in him.

Since Jesus always followed his Father's will and always did those things that pleased the Father, it was certainly pleasing to the Father that His son would become sin for man and die on the cross. This is precisely what God had asked him to do. While on the cross, Jesus Christ stated the words "It is finished" indicating that all that God had asked him to do was now complete. It was the summation of the work that had been requested of him and he had carried it out in every single detail. As a result of his work and the resurrection to follow, the redemption and salvation of mankind would be possible. This was the purpose that God had in mind for the life and death of His son. It was for this purpose that he had been kept or spared. His declaration on the cross was then simply a recognition of this reality.