Doing some grammar exercises I faced the following grammatically correct options. I want to understand the difference in meaning
I haven't been back to London since I've lived in Italy
I haven't eaten really good pasta since I lived in Italy_
and the last one which is grammatically correct, but like the book says "tells that it's difficult to find good pasta in Italy, which is not true"
I haven't eaten really good pasta since I've lived in Italy
What is the semantic difference between the first two sentences? Does the first one suggest that the teller still lives in Italy whereas the second suggests that the teller doesn't live in Italy anymore?