The people of Israel does not refer to all the Israelites, only those in Bethulia. With the beginning of a new section it will be helpful to begin the verse with “When the people in Bethulia saw Holofernes’ army, they….”
Cried out to the Lord their God may be rendered “asked the Lord their God to help them” (so Good News Translation, Contemporary English Version) or “asked the great ruler, the God whom they served, to help them.” For a comment on Lord, see Tob 3.2.
Their courage failed may be translated “they no longer believed that they could defeat the Assyrians.”
The literal all their enemies had surrounded them is somewhat awkward. The point is not that every one of their enemies is present, but that the enemy has them surrounded. Good News Translation‘s “with the enemy all around them” captures the idea well. In English “enemy” can be used collectively to refer to a group of soldiers who are enemies.
Quoted with permission from Bullard, Roger A. and Hatton, Howard A. A Handbook on Judith. (UBS Helps for Translators). New York: UBS, 2001. For this and other handbooks for translators see here.
