Abimelech wanted a treaty so that Abraham would not deceive him. He knew that God was blessing Abraham, even though Abraham had not always been truthful (20:9–10). This sad contradiction made the treaty necessary.
By contrast, God’s people are called to speak truthfully. Paul teaches believers to speak the truth in love (Ephesians 4:15, 25). Jesus also warned against using oaths to distort the truth (Matthew 5:37; James 5:12).