God who appeared to Moses is distinguished from God the Father
And so on, for I do not think fit to write over again the same words, having written them all before, but shall of necessity give those by which I established the proof to Trypho and his companions. Then I proceeded to what follows, in which these words are recorded:
Justin: 'And the Lord went His way as soon as He had left communing with Abraham; and [Abraham] went to his place. And there came two angels to Sodom at even. And Lot sat in the gate of Sodom;' and what follows until, 'But the men put forth their hands, and pulled Lot into the house to them, and shut to the door of the house;' and what follows till,
And the angels laid hold on his hand, and on the hand of his wife, and on the hands of his daughters, the Lord being merciful to him. And it came to pass, when they had brought them forth abroad, that they said, Save, save your life. Look not behind you, nor stay in all the neighbourhood; escape to the mountain, lest you be taken along with [them]. And Lot said to them, I beseech [You], O Lord, since Your servant has found grace in Your sight, and You have magnified Your righteousness, which You showest towards me in saving my life; but I cannot escape to the mountain, lest evil overtake me, and I die. Behold, this city is near to flee unto, and it is small: there I shall be safe, since it is small; and any soul shall live. And He said to him, Behold, I have accepted you also in this matter, so as not to destroy the city for which you have spoken. Make haste to save yourself there; for I shall not do anything till you have come there. Therefore he called the name of the city Segor (Zoar). The sun was risen upon the earth; and Lot entered into Segor (Zoar). And the Lord rained on Sodom and Gomorrha sulphur and fire from the Lord out of heaven; and He overthrew these cities, and all the neighbourhood.
Justin: (After another pause.) And now have you not perceived, my friends, that one of the three, who is both God and Lord, and ministers to Him who is in the heavens, is Lord of the two angels? For when [the angels] proceeded to Sodom, He remained behind, and communed with Abraham in the words recorded by Moses; and when He departed after the conversation, Abraham went back to his place. And when he came [to Sodom], the two angels no longer conversed with Lot, but Himself, as the Scripture makes evident; and He is the Lord who received commission from the Lord who [remains] in the heavens, i.e., the Maker of all things, to inflict upon Sodom and Gomorrha the [judgments] which the Scripture describes in these terms: 'The Lord rained down upon Sodom and Gomorrha sulphur and fire from the Lord out of heaven.'
Source: Dialogue with Trypho (New Advent)