“lifted up my hand.” A way of swearing an oath. See commentary on Ezekiel 20:5.
“I lifted up my hand and swore to give to your fathers.” One of the reasons that there must be a Millennial Kingdom, a future kingdom of Christ on earth, is that God swore to give the land of Israel to Abraham and his descendants. Yet Abraham never owned land in Israel (cp. Acts 7:5). Furthermore, between Israel’s failure to conquer the land under Joshua, and the fact that through much of Israel’s history part or all of the land was controlled by foreigners—the Philistines, Syrians, Assyrians, Babylonians, Persians, Greeks, Romans, and others—God’s promise that Israel would have the land has not been fulfilled. Yet God’s promise must be fulfilled; and it will be when Jesus Christ comes back to earth, fights the Battle of Armageddon, conquers the earth and gives the land of Israel back to the Israelites.