If we love God, we should obey Him (John 14:15). To love God first means to obey Him first—before looking at our neighbor. So, is the greater good trusting God when He says not to lie or trusting in our fallible, sinful minds about the uncertain future?
Consider this carefully. In the situation of a Nazi beating on the door, we have assumed a lie would save a life, but really we don't know. So, one would be opting to lie and disobey God without the certainty of saving a life—keeping in mind that all are ultimately condemned to die physically. Besides, whether one lied or not may not have stopped the Nazi solders from searching the house anyway.
As Christians, we need to keep in mind that Jesus Christ reigns. All authority has been given to Him (Matthew 28:18), and He sits on the throne of God at the right hand of the Father (Acts 2:33; Hebrews 8:1). Nothing can happen without His say. Even Satan could not touch Peter without Christ's approval (Luke 22:31). Regardless, if one were to lie or not, Jesus Christ is in control of timing every person's life and able to discern our motives. It is not for us to worry over what might become, but rather to place our faith and obedience in Christ and to let Him do the reigning. For we do not know the future, whereas God has been telling the end from the beginning (Isaiah 46:10).