With all that background, it is actually a bit surprising to me that so much of Lamsa's translation reads like the RSV. However, there are some interesting readings in Lamsa's version that deserve mention. For example, look at the first verse of Psalm 22 in the Lamsa version: "My God, my God, why hast thou let me to live? and yet thou hast delayed my salvation from me, because of the words of my folly." If we skip to the New Testament and Jesus' quote of Psalm 22 on the cross, the Lamsa version reads: "My God, my God, for this I was spared!" (with a footnote reading "This was my destiny"). These two quotes are quite different from most other English versions. I don't know why there is such a disparity in the OT and NT quotes; that would certainly be something to research further. But moving along...
In Matthew 19:24, the familiar quote about a camel going through the eye of a needle, we read: "Again I say to you, It is easier for a rope to go through the eye of a needle, than for a rich man to enter the kingdom of God." A footnote on this verse explains that "The Aramaic word gamla means rope and camel." Of course, if we go with the "rope" reading, as Lamsa has done, the hyperbole Jesus uses is not quite as extreme as the traditional reading. Does it make a difference to the ultimate meaning, though? I doubt it.
Just skimming a couple other famous texts, I notice that the familiar "name in vain" verse from Exodus 20 becomes "you shall not take a false oath in the name of the LORD your God." I think this is rather interesting, as it clarifies a bit what "taking the Lord's name in vain" is, something that I think is pretty misunderstood in our modern Christian culture. The Prologue to the Gospel of John is just a bit different: "The Word was in the beginning, and that very Word was with God, and God was that Word."
As I said above, even though I've had a copy of Lamsa's translation of the Peshitta, I haven't really read it much. Just browsing through it to write this post, I think I should give it some more attention in the near future. Connecting to an ancient Eastern tradition can be a useful exercise, especially for modern American Christians, who often tend to think of Christianity as a Western religion. It's worth keeping in mind that the Syriac Church goes back much further than any European church. Incidentally, you can read the Lamsa version online here.