Whether God the Trinity Indiscriminately Appeared to the Fathers, or Any One Person of the Trinity. The Appearing of God to Adam. Of the Same Appearance. The Vision to Abraham
19 Likewise, also, in that which is written, “Now the Lord had said unto Abraham, Get you out of your country, and from your kindred, and your father's house,” it is not clear whether a voice alone came to the ears of Abraham, or whether anything also appeared to his eyes. But a little while after, it is somewhat more clearly said, “And the Lord appeared unto Abraham, and said, Unto your seed will I give this land.” But neither there is it expressly said in what form God appeared to him, or whether the Father, or the Son, or the Holy Spirit appeared to him.
Unless, perhaps, they think that it was the Son who appeared to Abraham, because it is not written, God appeared to him, but “the Lord appeared to him.” For the Son seems to be called the Lord as though the name was appropriated to Him; as e.g. the apostle says, “For though there be that are called gods, whether in heaven or in earth, (as there be gods many and lords many,) but to us there is but one God, the Father, of whom are all things, and we in Him; and one Lord Jesus Christ, by whom are all things, and we by Him.” But since it is found that God the Father also is called Lord in many places—for instance, “The Lord has said unto me, You are my Son; this day have I begotten You;” and again, “The Lord said unto my Lord, Sit at my right hand;” since also the Holy Spirit is found to be called Lord, as where the apostle says, “Now the Lord is that Spirit;” and then, lest any one should think the Son to be signified, and to be called the Spirit on account of His incorporeal substance, has gone on to say, “And where the Spirit of the Lord is, there is liberty;” and no one ever doubted the Spirit of the Lord to be the Holy Spirit: therefore, neither here does it appear plainly whether it was any person of the Trinity that appeared to Abraham, or God Himself the Trinity, of which one God it is said, “You shall fear the Lord your God, and Him only shall you serve.” But under the oak at Mamre he saw three men, whom he invited, and hospitably received, and ministered to them as they feasted. Yet Scripture at the beginning of that narrative does not say, three men appeared to him, but, “The Lord appeared to him.” And then, setting forth in due order after what manner the Lord appeared to him, it has added the account of the three men, whom Abraham invites to his hospitality in the plural number, and afterwards speaks to them in the singular number as one; and as one He promises him a son by Sara, viz. the one whom the Scripture calls Lord, as in the beginning of the same narrative, “The Lord,” it says, “appeared to Abraham.” He invites them then, and washes their feet, and leads them forth at their departure, as though they were men; but he speaks as with the Lord God, whether when a son is promised to him, or when the destruction is shown to him that was impending over Sodom.
Source: On the Holy Trinity (New Advent)