No.
"Then God is not omnipotent."
God is omnipotent.
"How can that be?"
Now that is a good question. Let us take this step by step. If you knew God, you would have immediately realized that He is both the Sovereign Lord and the Immovable Rock. So then God cannot create an immovable rock simply because God cannot be created.
As for the second question, "can God lift that immovable Rock?" Yes He can, in such a way that it would not be moved. What do I mean? I mean that God, in His infinite wisdom, will find a way to display His character even in seemingly conflicting situations.
For example, God declares Himself in the Bible as
the Rock and the Living Water
the Living Water and the consuming fire
The Prince of Peace and the Lord of War
He who creates and He who destroys
He who prospers and He who sends calamities
He who gives and He who takes away
The Lion and the Lamb
The King and the Servant
The High Priest and the Sacrifice
The Judge and the Mediator
among a host of other descriptions. But perhaps the outright clash of His qualities with regard to the human condition is best expressed in Exodus 34:6-7
6 And he passed in front of Moses, proclaiming, “The Lord, the Lord, the compassionate and gracious God, slow to anger, abounding in love and faithfulness, 7 maintaining love to thousands, and forgiving wickedness, rebellion and sin. Yet he does not leave the guilty unpunished; he punishes the children and their children for the sin of the parents to the third and fourth generation.”
Now, consider your case you sinner, whoever you are. Based on this text, what would God do to you? Would He forgive your sin, or would He punish you? Obviously, if He punished you then He had not forgiven. If He forgave you of your sins, then He cannot punish you because punishing you further would make Him unjust and cruel. There is an outright clash between God's mercy and justice.
Now what God did is this: God sent His Son, in whom His fullness dwells, to become flesh so that the Son would not only be the representative of the whole humanity, but as a substitute for sin (see God the Sacrifice below), "that whoever believes in Him shall not perish, but have everlasting life." Through God's way, in the very act of punishment, God was extending mercy to us.
Bottom line: God, in His infinite wisdom, will find a way to display His character even in seemingly conflicting situations. I do not know, nor will I claim to know how God will lift the immovable Rock. But I affirm that He can display both omnipotence and His immutability in a conflicting situation if He pleases.
Read more from Scripture:
God is the Sovereign Lord: Is 14:27
God is the Immovable Rock: 2 Sam 23:3, Acts 4:11, Psalm 18:1-2
God is the Living Water: Jeremiah 2:13,
God the Prince of Peace: Is 9:6
God the Lord of War: Ex 15:3
God prospers and creates disaster: Is 45:6-7
God the Sacrifice: 2 Cor 5:21
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haha sorry I don't have time right now. I'll just add the lacking Scripture references later if I remember and if I have time. Regardless, they're fairly easy to find especially with online Bibles :) Please do comment if you find them. Help is appreciated ;)