Was the Lord with whom Abraham negotiated material or Holistic? In Genesis chapter 18 Abraham negotiated with one of the three men who came to his tent. 

Verse 18:20 refers to that individual as 'LORD' , and only two of those are called Angels and go on to Sodom.

Since all things material were created by God in Genesis chapter 1, using the word 'Lord' would seem to indicate that that being was non material.

And yet we know that Abraham saw three men, that leads me to wonder if that one with which Abraham negotiated were an apparition.

I was further intrigued by the fact the other two (who are referred to as Angels) continued to Sodom while the  'LORD' did not.

What do Theologians say about this?
It was the understanding of many Church Fathers from the early Christians that the LORD who appeared to Abraham, Jacob, Moses and the prophets was Jesus Christ, the word of God, who is distinct from God the Creator.

In "The Dialogue with Trypho" written by Justin Martyr(100-165 AD), Justin explained to Trypho the Jew that one of the three men who visited Abraham was God in human form, who is distinct from God the Creator. Justin said that it was Jesus Christ, who appeared to Abraham, Jacob and Moses, who is called "LORD" in the Scripture, and recorded by Moses in the Scripture.


  Dialogue with Trypho, CHAPTER LVI
  
  I replied again, "If I could not have proved to you from the
  Scriptures that one of those three is God, and is called Angel,
  because, as I already said, He brings messages to those to whom God
  the Maker of all things wishes[messages to be brought], then in regard
  to Him who appeared to Abraham on earth in human form in like manner
  as the two angels who came with Him, and who was God even before the
  creation of the world, it were reasonable for you to entertain the
  same belief as is entertained by the whole of your nation." 
  
  "Assuredly," he said, "for up to this moment this has been our
  belief."
  
  Then I replied, "Reverting to the Scriptures, I shall endeavour to
  persuade you, that He who is said to have appeared to Abraham, and to
  Jacob, and to Moses, and who is called God, is distinct from Him who
  made all things,--numerically, I mean, not[distinct] in will. For I
  affirm that He has never at any time done anything which He who made
  the world--above whom there is no other God--has not wished Him both
  to do and to engage Himself with."