OH my GOSH! I am imagining my T in that situation and it would be.. wow. You described the reactions I would have really, really well!
In one sense, it would be really really difficult to see T struggling in that way. I would be angry at the lecturer for being so harsh! And I'd feel embarrassed for T, too! In another sense though, like you said, it would be a way to connect with T and see her humanity.
I've never seen my T in this kind of situation, but T has said things to me about how nervous she gets sometimes (she was trying to normalize my social anxiety) and that she blushes and gets blotches all over when she is feeling very shy. Sometimes I can tell in session if she's not sure what is the right thing to say because she stammers a little. It is sweet though and knowing about her anxiety makes me want to keep her safe somehow.. I bet she would blush and stammer in that situation pretty badly. If I were in your situation I would have had such a hard time NOT standing up for T, even though it's not really appropriate. That lecturer sounds pretty insensitive! Plus how awkward for your T, knowing she had a client in the audience too!
You sound like you are handling it well, though, griffin.

When are you going to see your T next?