Isaiah 11:1: "There shall come forth a shoot from the stump of Jesse, and a branch from his roots shall bear fruit."
Isaiah 11:6-10: "The wolf shall dwell with the lamb, and the leopard shall lie down with the young goat, and the calf and the lion and the fattened calf together; and a little child shall lead them. The cow and the bear shall graze; their young shall lie down together; and the lion shall eat straw like the ox. The nursing child shall play over the hole of the cobra, and the weaned child shall put his hand on the adder's den. They shall not hurt or destroy in all my holy mountain; for the earth shall be full of the knowledge of the LORD as the waters cover the sea. In that day the root of Jesse, who shall stand as a signal for the peoples - of him shall the nations inquire, and his resting place shall be glorious."
Isaiah 11:12-16: "He will raise a signal for the nations and will assemble the banished of Israel, and gather the dispersed of Judah from the four corners of the earth. The jealousy of Ephraim shall depart, and those who harass Judah shall be cut off; Ephraim shall not be jealous of Judah, and Judah shall not harass Ephraim. But they shall swoop down on the shoulder of the Philistines in the west, and together they shall plunder the people of the east. They shall put out their hand against Edom and Moab, and the Ammonites shall obey them. And the LORD will utterly destroy the tongue of the Sea of Egypt, and will wave his hand over the River with his scorching breath, and strike it into seven channels, and he will lead people across in sandals. And there will be a highway from Assyria for the remnant that remains of his people, as there was for Israel when they came up from the land of Egypt."
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The first verse ("Where tame live with the wild; / The lamb and lion side by side, / Led by a little child!") comes from Isaiah 11:6-10. The second verse comes from Isaiah 11:1; to some degree, it even keeps the parallel structure: "A shoot will sprout from Jesse's stem, / A branch from David's line."
The third and fourth verses seem to come from Isaiah 11:12-16, although - unlike the other two texts cited - there isn't a strong similarity as far as specific words and phrases. "He will raise a signal for the nations and will assemble the banished of Israel" seems to be the origin of "by His death a dying world / Would rally to the cross" in verse three. Jesus' leading His people to "Lost Paradise restore[d] / Lead[ing] past the angel's flaming sword" (in verse four) certainly resembles the end of Isaiah 11:12-16.
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The beginning of verse three ("As banner of God's love unfurled, / Christ came to suffer loss") has some resemblance to Song of Solomon 2:4: "He brought me to the banqueting house, and his banner over me was love." Both mention banners of love. I'm not sure if there's a real connection here or if it's just that the language is similar.
"The angel's flaming sword" in verse four is from Genesis 3:24: "He [God] drove out the man, and at the east of the garden of Eden he placed the cherubim and a flaming sword that turned every way to guard the way to the tree of life." While there's a single angel in the hymn but multiple angels (cherubim is the plural) in Genesis, this is clearly a passage that the hymn references. The titular first line further evidences this: "What hope! An Eden prophesied." However, rather than the actual Eden in Genesis, the hymn describes the "Lost Paradise restore[d]."
