If Jesus prayed Father, leave them (ἄφετε αὐτούς), for they don’t know what they are doing, as He was crucified rather than Father, forgive them (αφες αυτοις), for they don’t know (οἴδασιν, a form of εἴδω) what they are doing (ποιοῦσιν, a form of ποιέω), that’s a big difference, too big to turn on the translation of one word (αφετε and αφες are forms of ἀφίημι).  Yet that seems to be my only choice when comparing Luke 23:34 with Matthew 15:14.

In Matthew 15:14 (NET) Jesus spoke to his disciples about the Pharisees, Leave (ἄφετε, a form of ἀφίημι) them!  They are blind guides.  If someone who is blind leads another who is blind, both will fall into a pit.  In Luke 23:34 the Greek word εἴδω is the knowledge gained by seeing.  In contemporary colloquial usage then the word might be translated, Father, forgive them, for they don’t [see] what they are doing.  Both suffer from a lack of vision on the path they have chosen.  But the disciples were told to leave the one and God was implored to forgive the other.

My religious mind is tempted to consider that Jesus actually prayed Father, [leave them], for they don’t know what they are doing for one reason, and one reason only.  It likes rules, laws, guidelines and principles, for others certainly, but even for itself.  Within the bounds of those rules, laws, guidelines and principles it feels safe and righteous.  Adherence to rules is its primary means of self-justification.  Without rules, laws, guidelines and principles it feels desperate and lost.  My religious mind expects Jesus to follow the rules, too, particularly the rule of ἀφίημι He inspired in 1 John 1:9 and 10 (if we confess our sins, he is faithful and righteous, forgiving us our sins) and articulated in Luke 17:3 and 4 (If he repents, forgive him).  But God did not bind Himself to rules when it comes to being gracious or showing mercy to humanity.

I will be gracious to whom I will be gracious, I will show mercy to whom I will show mercy¹ He said to Moses even after giving the law at Mount Sinai.  It makes sense then that the dying Son of God would not be constrained by the rule of ἀφίημι when he prayed for forgiveness for humanity to his Father the living God.  And John wrote (1 John 2:1, 2 NET):

(My little children, I am writing these things to you so that you may not sin [ἁμάρτητε, a form of ἁμαρτάνω].)  But if anyone does sin (ἁμάρτῃ, another form of ἁμαρτάνω), we have an advocate (παράκλητον, a form of παράκλητος) with the Father, Jesus Christ the righteous One (δίκαιον, a form of δίκαιος), and he himself is the atoning sacrifice (ἱλασμός) for our sins (ἁμαρτιῶν, a form of ἁμαρτία), and not only for our sins but also for the whole world.

Paul wrote (Romans 8:31-39 NET):

What then shall we say about these things?  If God is for us, who can be against us?  Indeed, he who did not spare his own Son, but² gave him up for us all – how will he not also, along with him, freely give us all things?  Who will bring any charge against God’s elect?  It is God who justifies.  Who is the one who will condemn?  Christ is the one who died (and more than that,³ he was raised), who is at the right hand of God, and who also is interceding for us.  Who will separate us from the love of Christ?  Will trouble, or distress, or persecution, or famine, or nakedness, or danger, or sword?  As it is written, “For your sake we encounter death all day long; we were considered as sheep to be slaughtered (See Table1 below) [Table].”  No, in all these things we have complete victory through him who loved us!  For I am convinced that neither death, nor life, nor angels, nor heavenly rulers, nor things that are present, nor things to come, nor powers, nor height, nor depth, nor anything else in creation will be able to separate us from the love of God in Christ Jesus our Lord.

But I would like to know what Jesus thought about it.  Interestingly, He left enough clues to indicate what He was thinking and what He was believing, the literal content of the faith that sustained Him as He died on the cross.  At about three⁴ o’clock Jesus shouted with a loud voice, “Eli, Eli, lema⁵ sabachthani?” that is, “My God, my God, why have you forsaken me?”⁶  This is the first line of Psalm 22 (See Table2 below).  When he had received the sour wine, Jesus said, “It is completed!”  Then he bowed his head and gave up his spirit.⁷ Completion or accomplishment of salvation is the last thought of Psalm 22 (NET).

My God, my God, why have you abandoned me?
I groan in prayer, but help seems far away [Table].
My God, I cry out during the day,
but you do not answer,
and during the night my prayers do not let up [Table].

You are holy;
you sit as king receiving the praises of Israel [Table].
In you our ancestors trusted;
they trusted in you and you rescued them [Table].
To you they cried out, and they were saved;
in you they trusted and they were not disappointed [Table].

But I am a worm, not a man;
people insult me and despise me [Table].
All who see me taunt me;
they mock me and shake their heads [Table].
They say,
“Commit yourself to the Lord!
Let the Lord rescue him!
Let the Lord deliver him, for he delights in him [Table].”

Yes, you are the one who brought me out from the womb
and made me feel secure on my mother’s breasts [Table].
I have been dependent on you since birth;
from the time I came out of my mother’s womb you have been my God [Table].
Do not remain far away from me,
for trouble is near and I have no one to help me [Table].

Many bulls surround me;
powerful bulls of Bashan hem me in [Table].
They open their mouths to devour me
like a roaring lion that rips its prey [Table].
My strength drains away like water;
all my bones are dislocated;
my heart is like wax;
it melts away inside me [Table].
The roof of my mouth is as dry as a piece of pottery;
my tongue sticks to my gums.

You set me in the dust of death [Table].
Yes, wild dogs surround me –
a gang of evil men crowd around me;
like a lion they pin my hands and feet [Table].
I can count all my bones;
my enemies are gloating over me in triumph [Table].
They are dividing up my clothes among themselves;
they are rolling dice for my garments [Table].

But you, O Lord, do not remain far away!
You are my source of strength!  Hurry and help me [Table]!
Deliver me from the sword!
Save my life from the claws of the wild dogs [Table]!
Rescue me from the mouth of the lion,
and from the horns of the wild oxen!

You have answered me! [Table]

I will declare your name to my countrymen!
In the middle of the assembly I will praise you! [Table]
You loyal followers of the Lord, praise him!
All you descendants of Jacob, honor him!
All you descendants of Israel, stand in awe of him! [Table]
For he did not despise or detest the suffering of the oppressed;
he did not ignore him;
when he cried out to him, he responded [Table].

You are the reason I offer praise in the great assembly;
I will fulfill my promises before the Lord’s loyal followers [Table].
Let the oppressed eat and be filled!
Let those who seek his help praise the Lord!
May you live forever! [Table]

Let all the people of the earth acknowledge the Lord and turn to him!

Let all the nations worship you! [Table]
For the Lord is king
and rules over the nations [Table].
All of the thriving people of the earth will join the celebration and worship;
all those who are descending into the grave will bow before him,
including those who cannot preserve their lives [Table].
A whole generation will serve him;
they will tell the next generation about the sovereign Lord [Table].
They will come and tell about his saving deeds;
they will tell a future generation what he has accomplished [Table].

Here is the forgiveness, the mercy, the grace and salvation of God in Jesus the Christ.  I do not doubt that Jesus prayed, Father, forgive them, for they don’t know what they are doing.

Addendum: October 12, 2018
Tables comparing the Greek of the Old Testament quotation in Romans 8:36b with Psalm 44:22 and that in Matthew 27:46 with Psalm 22:1a in the Septuagint, and tables of Romans 8:32; 8:34 and Matthew 27:46 comparing the NET and KJV follow.