Let’s begin understanding this name, /Adonai/ (אֲדֹנָי), meaning /Lord/, by going back to the Middle Ages. Picture a medieval manor. Peasants worked the surrounding fields. Craftsmen lived in the village. The manor house, maybe with a moat and watchtower, dominated the landscape. There the lord of the manor lived. He ruled over the surrounding land and people. They were his subjects, his vassals. He was to keep them safe, guarding and protecting them, administrating justice, keeping the peace. They brought their petitions to him.
But a medieval lord ruled only a limited territory. Other lords were his equal. Often he was subject to a king. How much greater the Lord, /Adonai/ (אֲדֹנָי), with whom Abraham pleaded! Abraham addresses him as "the Judge of all the earth" (Genesis 18:25 NIV). He rules over all in heaven above and on earth below. Nothing is beyond his jurisdiction. Everything is under his justice. No one is his equal. No king is above him. For he is the King of kings and Lord of lords. /Adonai/ (אֲדֹנָי)!
He even rules over the wicked and rebellious. He had every right and authority to go down to Sodom and Gomorrah and mete out his justice. For all belongs to him. He is /Adonai/ (אֲדֹנָי), the Lord of all.