Some people get touchy when you question or try to refine the Trinity doctrine. Roman Catholic and Orthodox people are like that, even many Protestants. They are still ruled by the fear that they will be outcast as heretics (or even put to death as some were) if they are perceived to deny a central tenet of the faith.
When Lee says "The traditional explanation of the Trinity is grossly inadequate and borders on tritheism", he is not arguing for discarding the Trinity doctrine and embracing modalism. He is shifting the balance away from a model which borders on tritheism. As this website says there are different models of the Trinity -
http://reknew.org/2007/12/what-are-t...f-the-trinity/
Like Witness Lee, Augustine believed a version of the Trinity that some would say borders on modalism, that the 3 Persons are different aspects of the one Person. Yet Augustine is still a widely respected early church Father in Protestantism. Based on this, to say Augustine was a modalist is silly, he clearly affirms the 3 person Godhead, as Lee does also.
We should also note that the Trinity doctrine took years to evolve. If we look into early church writings we will discover that the formulaic version of the Trinity "in the Father, Son and Spirit", was not common place. Sometimes only one of the 3 was used, or two of the three. Sometimes they would just say "God", which can refer to either one of the 3 persons, or to the whole Godhead. If we lived in the time of the apostles and asked them about the Trinity they would not know what we are talking about - they had not yet formulated or specified an exact doctrine about it. However many years later the Trinity doctrine was formulated from all of the evidence available - the apostles and early Christians held the ideas and beliefs that form the basis of the Trinity doctrine that we know today.
We should realize what the Trinity doctrine is. The Trinity doctrine is a model invented by humans. A model is something that humans use to more easily explain and analyze complex things, such as God. As a model, it can never be 100% accurate or detailed in every respect. The limitation on the model's accuracy is what we do not know or cannot explain or understand. In the early days of the church, people's faith in God was judged by whether or not they accepted the model, some were even killed for it. The reason for that was not just because they wanted to be right about the nature of God, but because the alternative models (modalism etc), denied the Lord Jesus's divinity and rightful place as the son of God, even God Himself in human form. As it is just a model I do not see why it is a problem to refine it or question it as long as we maintain the reasons why it was developed in the first place - to defend Christ's nature. Jews, Muslims, JW's, and others who deny the Trinity, do so because they do not accept the divinity of the Son. However there is still room for improvement in the Trinity model. What many Christians may not know is that the exact relationship between the 3 Persons of the Trinity was never accurately defined. I suppose this was because the main purpose of defining the Trinity in the first place was to counter heresies at the time to do with the nature of Christ and whether or not he was God or just a man, or was he fully God or just half a God.
One aspect of the relationship between the 3 Persons, is about whether they are all present with 1, or whether they can separate themselves in space and time.
For one reason or another it is a common belief in Christianity that the Father stayed in heaven and he sent Christ to Earth. This view says that it is possible for them to be separated.
Not only is this denying the omnipresence of God, but Christ's own words: "John 8:29 The one who sent me is with me; he has not left me alone, for I always do what pleases him.". I believe Lee is right when he says the Father sent the Son but also was present with the Son. Christ also said "My God, my God, why have you forsaken me?" indicating that the Father's presence departed from him.
Although Jesus taught the Lord's prayer to pray to the Father, this is not to the exclusion of praying to the Son. There are examples in the Bible of the disciples praying to Christ. The name of Christ was upheld and used often. The "it is wrong to pray to Jesus" movement is clearly wrong. To not pray to Jesus says that he is not really God. For example the Jehovah’s Witnesses will not pray to Jesus because they think that He is not worthy of worship.
The Bible never goes into great detail about whether or not all 3 were present on the cross, or whether only 2 are is heaven and 1 is on earth, etc. From the Bible it is possible to construct a doctrine that the Father was in Heaven, the Son was on Earth and the Spirit came to Earth only after Pentecost. It is also possible to construct a doctrine which says that all three were present on the Earth at the same time - God is omniscient.