The OP asks why did Jesus lift up His eyes to the sky to address God?
The OP also suggests some possible answers:
Is God in the sky? Is God always "up", no matter where on earth you are? Or should those on the opposite side of the earth look down? What about day vs night?
Since Jesus was Jewish, the answer should be considered in the light of Jewish practices.
In Solomon’s prayer dedicating the Temple he specifically asked that prayers directed toward the Temple be heard and answered:
that Your eyes may be open toward this temple night and day, toward the place of which You said, ‘My name shall be there,’ that You may hear the prayer which Your servant makes toward this place. (1 Kings 8:29) 1
Solomon enumerates seven situations where prayer toward or in the Temple should be made and heard (vv 30, 33, 35, 38, 42, 44, and 48).
Scripture gives examples this was the practice. It is how Jonah prayed:
...Yet I will look again toward Your holy temple.’ (Jonah 2:4)
“When my soul fainted within me,
I remembered the LORD;
And my prayer went up to You,
Into Your holy temple. (Jonah 2:7)
It is how Daniel prayed:
Now when Daniel knew that the writing was signed, he went home. And in his upper room, with his windows open toward Jerusalem, he knelt down on his knees three times that day, and prayed and gave thanks before his God, as was his custom since early days. (Daniel 6:10)
Following Solomon's prayer dedicating the Temple, the custom was to direct prayer toward the Temple. The Babylonian Talmud Tractate Berakoth [Berakoth Folio 30a] records the teaching of how where one should look to direct their prayers:
- The blind who cannot tell direction should pray toward His Father in heaven
- If outside the land, face Israel
- If in Israel but away from Jerusalem, face Jerusalem
- If in Jerusalem, face the santuary
- If in the Sanctuary, face the Holy of Holies
- If in the Holy of Holies, face the mercy-seat
Jesus is in Jerusalem; the Temple is still standing. He should be making His prayer toward the location of the Sanctuary.
By looking toward heaven He is indicating the correct location of the Temple:
But Christ came as High Priest of the good things to come, with the greater and more perfect tabernacle not made with hands, that is, not of this creation. (Hebrews 9:11)
And the future location of the Temple:
But He was speaking of the temple of His body. Therefore, when He had risen from the dead, His disciples remembered that He had said this to them; and they believed the Scripture and the word which Jesus had said. (John 2:21-22)
Now this is the main point of the things we are saying: We have such a High Priest, who is seated at the right hand of the throne of the Majesty in the heavens, (Hebrews 8:1)
His body is now the True Temple.
Finally, when considering this question in the light of what Jesus taught, there is additional significance. Jesus said He would give the sing of Jonah. In essence Jesus is modeling the content of what Jonah prayed:
Then I said, ‘I have been cast out of Your sight;
Yet I will look again toward Your holy temple.’ (2:4)
“When my soul fainted within me,
I remembered the LORD;
And my prayer went up to You,
Into Your holy temple. “Those who regard worthless idols
Forsake their own Mercy. But I will sacrifice to You
With the voice of thanksgiving;
I will pay what I have vowed.
Salvation is of the LORD.” (2:7-9)
1. All Scripture from the New King James Version