From the narrative, we are left to discern for ourselves the identity of the individual with whom they conversed. It is not hard to imagine that they were speaking to the Lord--even as Moses did when he was transfigured, and ‘the skin of his face shone while he talked with him’ (Ex 34:29). Aminadab’s interpretation of events was that they were speaking with angels (v. 39). This observation is much like that of Nebuchadnezzar and the story of Shadrach, Meshach, and Abed-nego. The three righteous Jews were cast into a burning furnace but remained unscathed. Nebuchadnezzar saw a fourth individual in the midst of the flames who he referred to as an “angel”, although, in reality, the “angel” was Jehovah, ‘the form of the fourth is like the Son of God’ (Daniel 3:25-28). In conclusion, Moses conversed with Jehovah, Shadrach, Meshach, and Abed-nego were preserved by the pre-mortal Savior himself, and Nephi and Lehi were also conversing with Jehovah, but to do so they first had to be transfigured.
Bruce R. McConkie
"Transfiguration is a special change in appearance and nature which is wrought upon a person or thing by the power of God. This divine transformation is from a lower to a higher state; it results in a more exalted, impressive, and glorious condition…
"By the power of the Holy Ghost many prophets have been transfigured so as to stand in the presence of God and view the visions of eternity. Speaking of such an occasion in his life, Moses recorded: ’Now mine own eyes have beheld God; but not my natural, but my spiritual eyes, for my natural eyes could not have beheld; for I should have withered and died in his presence; but his glory was upon me; and I beheld his face, for I was transfigured before him.’ (Moses 1:11; D. & C. 67:11.) On another occasion, when Moses came down off the mount, having communed with the Lord for 10 days and nights, ’the skin of his face shone,‘ so that he had to ’put a vail on his face’ as he talked with the children of Israel. (Ex. 34:29-35.)
“Similarly, when the Three Nephites ’were caught up into heaven, and saw and heard unspeakable things,’ they were transfigured. ’Whether they were in the body or out of the body, they could not tell; for it did seem unto them like a transfiguration of them, that they were changed from this body of flesh into an immortal state, that they could behold the things of God.’ (3 Ne. 28:13-17.) Paul had a similar experience (2 Cor. 12:1-4), as also did Joseph Smith and Sidney Rigdon. (D. & C. 76; Teachings, p. 107.)” (Mormon Doctrine, p. 803)