Lamsa is also not a scholar, but a psuedo-scholar.
That is obviously disputable.
The problem with the whole 'Peshitta primacy' argument is that it requires a Protestant worldview; that of a pristine text from the beginnings (or as the beginnings) of the Church.
If that were true, why would Peshitta primacy be the official teaching of the Assyrian Church of the East?
That is what the argument is really about for the Aramaic Primacists - their claim that Greek is bad, unknown, contrary to Christianity.
I have not seen or heard any Aramaic primacist who has actually made that claim. The argument made is that the New Testament was originally written by Semitic-speaking people, for Semitic-speaking people, and about Semitic-speaking people, and therefore would not have been written in Greek. The question of whether or not the Apostles spoke fluent Greek is beside the point.
The question is what would have been the best language to reach the lost tribes of Israel, who were to be the first receivers of the Gospel message. Numerous times, both Jesus and Saint Paul state that their mission was first for the lost tribes and then
the Gentiles. I do not doubt that, early on, Greek versions of the New Testament works were created as to reach the non-Semitic peoples.
That does not mean, however, that Greek was the original language.
There are numerous internal evidences within the New Testament that point to an Aramaic original. For example, while John 12:20 in most English Bibles reads that Jesus was visited by Greeks, the Peshitta more accurately reads that they were Gentiles. This is more in keeping with Eusebius' account that the Prince of Edessa had sent representatives in order to learn of Jesus' mission: http://www.biblefacts.org/church/edessa.html
As a descendent of the lost tribes, Abgarus wanted to know whether Jesus was the promised Messiah. Furthermore, early on, the Syriac peoples converted to the Christian faith. It is hard to believe that a Syriac version of the New Testament did not exist until centuries later.