1 and 2 have similar meanings. Use them to express she lived in Italy before another time/event in the past.
"When we visited Italy, we asked Chloe for recommendations because she had lived in Italy."
"She had been living in Italy for 3 years before she really felt confident in the language."
Had been living - used when you say 'how long'
Do not use 1 and 2 if there is no other time/event that happened afterwards. Just use past simple.
"She lived in Italy for ages so her Italian is pretty good "
3
An action in the past which continues up to now, or has very recently ended.
"I saw Chloe yesterday. I hadn't seen her in ages. Apparently, she's been living in Italy."
Chloe just recently returned from living in Italy
"Chloe has been living in Italy for 3 years."
Adding the 'how long' detail makes it clear that Chloe still lives in Italy and this began 3 years ago.