Yes, the battle is the Lord's, but God's protection is only for the faithful and obedient who are serving in His army. Its purpose was to buy atonement, or protective covering, for the ones who were going to war. Thus it spoke of covering the soldier's sin from the face of the holy, righteous God, so God could provide protection and victory for them as they fought the Lord's battles. This payment shows us that God's protective grace is not free, yet it is within reach of every man. It was not a progressive tax.
Grace is freely available to sinful man, but it had to be purchased.
Someone had to pay the price. Of course, we know that Christ paid that price. The men of Israel clearly understood the implication of this tax. Thus they recognized the Lord's providential protection of them in battle. It spoke of the Lord's protection as men fought in His warfare against evil.