i was thinking exactly like kakaze about it being just a demonstration to Lobsang. AND a demonstration to the readers as well

I totally agree. He was constantly teaching something to Lobsang, in his own way.
I don't understand however the last part of your post. What has it to do with susan and with the lifetimer? I don't remember any connection..
Another question , if i may
at the end, unity is dead dead, right? She's not going to come back, right? When Death says It's just the beginning or something like that, he talks about the afterlife, 'cause in the discworld everyone seems to have his own afterlife, based on whatever each of them really believe.
But what can Unity believe? She barely know what death is...
About Susan, her only friends, her only connection to the 'real' world are the children, because she can be herself with them, without being afraid of being judged for what she is. She wants to be a normal girl, but she is not, she can never be, and people would be scared knowing who she really is. But not the children. So she found her place in the world at first babysitting, and then teaching to children.
I love this about her. She is strong. She doesn't stop to cry "why why can't i be like everyone else why?" , she goes on and she finds her own place.
Another thing. It's funny that she keeps saying "i want to be normal" and then she takes such "un-normal" lessons, bringing the class in the sky and stuff like that. I loved that moment. Her real self, enjoying who she is.
p.s.if i make mistakes with the language, please tell me. i learned english with american movies and english books expecially TP's