Hi Jake!
I would say it's a good representative of the ancient Syriac Peshitta version (as you said), and valuable for comparison with the Greek text.
There were some chaps who took a position that the New Testament was originally written in Hebrew (I do not believe Aramaic), and that was better than the Greek. They were Biven and Blizzard. Their first book was not noteworthy.
But, as concerns the Aramaic of your friend, the OT was written in Hebrew (with a few small portions written in Aramaic -- such as in Daniel), and the New Testament in Greek, with apostolic authority and approval.
The woman through whose powerful witness to Christ I was converted (in 1968) used the Lamsa version.
I would tell the elderly lady in your class, privately, that you respect her view, but it is not the view you wish to promote in the class, and would she please humbly submit to the teaching authority of the church. She is probably a godly woman, and would comply.
P.S. Here's an example of an aberrant reading it contains:
In the AV's Matt 27:46 (cf. Mk 15:34) the Scripture reads:
And about the ninth hour Jesus cried with a loud voice, saying, Eli, Eli, lama sabachthani? that is to say, My God, my God, why hast thou forsaken me?
Jesus was echoing Psalm 22:1.
The Peshitta reads,
And about the ninth hour, Jesus cried out with a loud voice and said, Eli, Eli, lemana shabakthani! My God, my God, for this I was spared! [in margin: This was my destiny.]
The words in the AV were given as Jesus uttered them, in Aramaic. The Peshitta likewise mangles Psalm 22:1 beyond recognition.