Secrets of Heaven # 2186
2186. And he was standing before them under the tree symbolizes the perception that resulted. This follows from the symbolism of a tree as perception (discussed in §§103, 2163).
Above at verse 4, the three men who came to Abraham reclined under a tree, and it was said that this meant the Lord's divine side would move closer to his perceptive ability in the state he was then in [§2160]. Here, though, it says that Abraham stood under the tree, which means that the Lord moved closer to divine perception after he had prepared himself–a responding move of his own.
Anyone can see that the three men and Abraham would not both have been described as standing under the tree for no reason. They were described that way, then, for the sake of secrets lying hidden in the words.