1 And the Lord appeared to him by the oaks of Mamre, as he sat at the door of his tent in the heat of the day. 2 He lifted up his eyes and looked, and behold, three men were standing in front of him When he saw them, he ran from the tent door to meet them and bowed himself to the earth 3 and said, “O Lord, if I have found favor in your sight, do not pass by your servant. ESVJohn J. Davis notes, "Some commentators argue that the three men were the three persons of the trinity, but their argument is unconvincing."(21) Many passages cited by Trinitarians as evidence of multiple divine persons are in reality inconclusive. Such an interpretation is not certain nor necessary. Let's allow the inspired Bible writer to tell his own story.
As verse two makes clear Abraham thought they were men at first. He rushes to extend the typical hospitality and humility of the Oriental tradition by bowing and asking to wash their feet (18:2). He offers a respectful greeting and bows. His bowing to the visitors was nothing more than an expression of humility. Richard E. Friedman suggests these three "men" are all three angels. He notes, “Abraham can face three angels and address “my Lord.” And an angel can speak God’s words in first person or can speak about God in third person. All this is so because in some ways an angel is an identifiable thing itself, and in some ways it is merely a representation of divine presence in human affairs.” (23) I agree with Friedman here about first person and third person language. However, I disagree that all three men were really angels.
In 18:3 Abraham says, "if I have found favor in your sight". This is actually common when used to reference someone of a higher rank or to honor someone. Laban (Gen. 30:27), Jacob (32:5) Shechem (Gen. 34:11) and the Egyptians (Gen. 47:25) all used this same phrase. This alone is no evidence of a theophany or even an angel at this point. However, perhaps Abraham did not immediately recognize who his guests truly were. It seems though Abraham and Sarah were indeed visited by the LORD Himself. In 18:12-13 the LORD discerns Sara's inner laughter and asks if anything is "too hard" for the LORD?
In verse 13 we read, “The Lord said to Abraham, “Why did Sarah laugh and say, ‘Shall I indeed bear a child, now that I am old?’” (18:13, ESV) Here the Lord, alone, speaks to Abraham. This becomes even more clear as we reach verse 22 where we read, “22 So the men turned from there and went toward Sodom, but Abraham still stood before the Lord.” (18:22, ESV) The term “Lord” here is used throughout this chapter as an obvious and specific reference to God and not the other two angels. Only one of them is recognized as true LORD while the others are angels. These two angels eventually leave Abraham and are the very two who later appear to Lot in the next chapter (Gen. 19:1) to bring judgement to Sodom (Gen. 19:12-13).
22) See Wenham, G. J. (2002). Vol. 2: Word Biblical Commentary : Genesis 16-50. Word Biblical Commentary (45). Dallas: Word, Incorporated. - Reyburn, W. D., &amp; Fry, E. M. (1997). A handbook on Genesis. UBS handbook series (384). New York: United Bible Societies.
23) Friedman, Richard E. (2001) Commentary on Torah. (63) New York, NY: Harper Collins Publishers.
24) Lapide, Pinchas. (2002) Jewish Monotheism and Christian Trinitarian Doctrine. A Dialogue by Pinchas Lapide and Jurgen Moltmann. Eugene, Oregon: Wiipf and Stock Publishers
25) See Keil, C. F., &amp; Delitzsch, F. (2002). Commentary on the Old Testament. (Ge 18:1–15). Peabody, MA: Hendrickson. - Davis, John J (1975). Paradise to Prison (196) Salem, Wisconsin. Sheffield Publishing Company. - Carson, D. A. (1994). New Bible commentary : 21st century edition (4th ed.) (Ge 18:1–15). Leicester, England; Downers Grove, Ill., USA: Inter-Varsity Press. - Whitlock, L. G., Sproul, R. C., Waltke, B. K., &amp; Silva, M. (1995). Reformation study Bible, the : Bringing the light of the Reformation to Scripture : New King James Version (Ge 18:2). Nashville: T. Nelson. - Reyburn, W. D., &amp; Fry, E. M. (1997). A handbook on Genesis. UBS handbook series (385). New York: United Bible Societies.