“And my tongue sticks to the roof of my mouth.” This certainly literally applied to Jesus. It is very likely that Jesus was so dehydrated that his tongue had swollen and he could not talk well. He had been arrested on Monday night and it was now Wednesday morning, and besides that, he would have bled a lot from the beatings and being whipped and being nailed to a cross. This was likely why when he said “Eli, Eli, lama sabachthani?” (Matt. 27:46) that the people mistook him for calling for Elijah instead of God (Matt. 27:47). It is also why he said, “I am thirsty” (John 19:28). [For more on the events of Jesus’ last week, including his arrest on Monday night through his crucifixion Wednesday morning, see commentary on John 18:13].
“you lay me in the dust of death.” The verb “lay” is in the imperfect in the Hebrew text, indicating that the action was then occurring. The Psalmist was not yet dead, which we can tell because he is still speaking. We know that Christ did die, and was in the process of dying while he was on the cross. In contrast, David did not die, but would have felt he was in the process of dying because of being hounded and pursued by Saul. The Psalm could be taken to imply that the psalmist died, but that is not explicitly stated (cp. NET text note; Allen Ross, A commentary on the Psalms). Thus, the Jews never got from Psalm 22 that the Messiah would die.