The icon of Jesus sleeping was popularized in Greece and the Balkans in the 13th century.
The name of this icon comes from the prophecy of Jacob before his death. He said to his son Judah:
Judah is a lion’s whelp. From a tender shoot, my son, you have gone up. He crouches down, he stretches out like a lion, like a whelp. Who will rouse him? A ruler will not fail from Judah, nor a leader from his thighs, until the things laid up for him come, and he is the expectation of the nations. (Genesis 49:9-10)
This is one of the oldest prophecies of the coming of Christ, older than Moses and the other prophets.
According to St. John Chrysostom, the "tender plant" is the Virgin Theotokos, from which Jacob's son—Christ—went up. In the icon, the Theotokos supports the Lord as he sleeps.
The lion is an ancient symbol of royalty, and Christ is both the King himself, and the son of King David. For this reason, Christ is clothed in royal robes rather than swaddling clothes, and he lies on a royal bed rather than in a manger.
Jacob mentions "the things laid up for him," which refers to the Passion and the Cross; for this reason, two of the Angels hold the instruments of the Passion and the Cross. And referring to the Resurrection, Jacob says, "Who will rouse him?" Who indeed, but himself? As Christ says, "No one takes my life from me, but I lay it down myself. I have the power to lay it down, and I have power to take it again." (John 10:18)
St. John Chrysostom says in his homily Against Marcionists and Manichaeans:
As the lion is terrible not only when he is awake but even when he is sleeping, so Christ also not only before the cross but also on the cross itself and in the very moment of death was terrible, and wrought at that time great miracles, turning back the light of the sun, cleaving the rocks, shaking the earth, rending the veil... Darkness took hold of the earth, and night appeared at midday, then death was brought to nought, and his tyranny was destroyed. Many bodies of the saints which slept arose.
These things the patriarch Jacob declared beforehand, and demonstrating that, even when crucified, Christ would be terrible, said, 'you lay down and slumber as a lion.'
(Gloss from Orthodox Planet)