With the verb 'to read' it's quite easy for me to see the difference between 'I've read' and 'I have been reading' because you can read a few books during a year.
I don't quite follow your reasoning. Why does it matter that you can read several books in a year?
However, with the verb 'to live' or 'to work (at one particular place)' it's different. You can't live a few times. So the present perfect with 'to live' is not the same as with 'to read'.
I don't really understand this part at all. What does "You can't live a few times" mean?
Some more advanced students might want to know the difference in use between 'I've lived here for...' and 'I've been living here for...' and I used to tell such students that there is no difference.
Of course there's a difference, given by the fact that one of the sentences has an added aspect. Whether you feel this difference is something that you want to spend valuable class time on is another matter. Remember also to distinguish use from meaning.
Now I have some doubts about that. That's why I need some contrasting contexts to show this difference to these imaginary 'advanced' students (who can already feel the difference between 'I've read a few books this year' and 'I've been reading a lot this year', but cannot understand the difference between 'I've lived here all my life' and 'I've been living here all my life').
Unfortunately, I can't quite tell for sure what you want to know. Are you merely saying you need some very clear example contexts that show how present perfect continuous differs from present perfect simple? If you can help us understand exactly what it is that you don't understand or exactly what it is that you want advice on, then perhaps we can better help you.
Remember that state verbs behave differently from non-state verbs. In cases where you might ordinarily want to use a continuous aspect to frame time, it just doesn't work with state verbs:
I've been knowing her for twenty years.
I've known her for twenty years.
I've only been having my phone for a week.
I've only had my phone for a week.
Is this what you're getting at? The fact that some verbs have 'built into' their meanings a certain duration?