With Sacred Scripture, there are many levels of meaning at work. You are correct in observing that Jesus is quoting from Psalm 22. And many argue, with good merit, that quoting the first line of Psalm 22 Jesus intends the whole of Psalm 22 for himself, and us. 
 
In Psalm 22, we are alerted to the many ways in which prophecies are being fulfilled. The Psalm speaks of an afflicted man who feels downcast, but also mentions others who divide his garments among them, and cast lots for his vesture; who pierce his hands and feet; and who ridicule him in his suffering. And all these prophecies are being fulfilled almost exactly as Jesus is on the cross. 
 
Psalm 22 is also an important catechism for us about suffering because, considered as a whole, it is not a Psalm of despair and grief, but also of trust and hope in God's deliverance. It recalls how God has delivered devout men and women in the past, and asserts that God never spurns those who cry out to him in their misery. The psalm writer confidently expects God’s help, and to be able, one day, to tell his descendants of the glorious things the Lord has done. And thus, while Psalm 22 surely gives voice to the pain and grief that we experience in our suffering, it also reminds us to call on the Lord and trust that he will deliver us. 
 
And so, we see, first of all, that Jesus, in quoting Psalm 22, is a great teacher, even from the pulpit of the cross. We are taught to revere prophecy, and also to trust God in our afflictions. 
 
And yet we ought not to wholly exclude that Jesus is also quoting the psalm for his own sake as well. Surely, as man, he suffered great anguish, both physical and mental, emotional and spiritual, on the cross. And thus he, for his own sake, has recourse to Psalm 22. Indeed, how often have many of us in our sufferings found in Scripture great consolation and vindication. Perhaps we will say, "This scripture text expresses exactly how I'm feeling!" In this there is a kind of consolation that God knows what I am experiencing and that others have endured similar trials. We also experience consolation as Scripture teaches us how God has delivered others and will in due time deliver us too. Surely, at the human level, Psalm 22 consoled Jesus in these and other ways.

If, by artificial life support, you mean something such as a ventilator, the use of such machines is not required when they are no longer therapeutic, and the person is certainly dying. Neither is it required to revive a person who is approaching death each time their heart stops. 
 
Allowing someone to die whom the Lord is certainly calling is morally very different from directly causing a person to die, which is what euthanasia advocates claim the right to do. 
 
One exception to the non‐required use of artificial means is that food and water, even if supplied by a tube, should still be administered to those who are approaching death. Only in rare cases, where the major organs of the body have already shut down and can no longer process food or fluids, can this treatment be discontinued.