This is not an exact quote from scripture but rather a combination of thoughts from a couple of verses.
Isaiah 11:6 The wolf also shall dwell with the lamb, and the leopard shall lie down with the kid; and the calf and the young lion and the fatling together; and a little child shall lead them.
Isaiah 65:25 The wolf and the lamb shall feed together, and the lion shall eat straw like the bullock: and dust shall be the serpent's meat. They shall not hurt nor destroy in all my holy mountain, saith the LORD.
Both of these passages deal with the kingdom age on the earth after the Lord Jesus Christ returns to reign on the earth as King of kings. The ferocious beasts (like the lion) will live peaceably with the gentle animals (like the lamb). Certainly, this will be a literal reality on the earth. However, this picture is also symbolic of the peace that will pervade the entire earth. When preachers speak of the lion and the lamb lying down together, they are referring to the time of peace when Jesus will reign as King over the earth.