I was wondering this same thing. I googled it and this is what I found:
I think "immer noch" has a tendency to "has not stopped", whereas "noch" sounds a bit like "still, but may change in future".
Ich arbeite noch. - "I am still working (although I am going to stop working soon)."
Ich arbeite immer noch. - "I am still working (since this morning)" / "I have not stopped working."
"Er lebt" means "He is living/He is alive", while "Er lebt noch" means "He is still living/He is still alive". "Er lebt immer noch" puts a stronger emphasis on the "still". It's just taking a verb and adding some adverbs to it to change the meaning of the sentence a little bit. So you're correct that they technically both mean "He is alive", but the tone behind it and the specific meanings are different. Hope this helps!
Before, it stated the same idea as "Ich lebe noch" without the "immer". Is the meaning the same in either case? I understand "noch" to mean "another" and not "still", yet in that previous example it was used for "still"... is this just an exception/idiom to use "noch" this way?
This is probably a very silly question- i am only a beginner here, but if "wir leben noch" means " we're still alive", why is the word "immer" necessary when saying "he is still alive" ( "Er lebt immer noch"). Can somebody please shed some light on this for me? Thank you in advance!
Talking about a terrorist: Er lebt immer noch. Talking about a duck: Die Ente lebt noch.
Maybe that's when it's used with and without immer.