This term was introduced by Lambeth in its Culture 2020 Report, which is available at
Cabinet report
in the Full cabinet papers.
The report uses the following key definitions :-
"Healthy Living Centre" is a gym which has a lounge. [1]
"Neighbourhood Library" is a self-service facility in the gym's lounge offering "a small selection of books," [2], Wi-Fi access and computers. [3]
In other words a "neighbourhood library" would not be a library.
[1] Page 45 paragraph 7.9
[2] Page 154
[3] Page 30 paragraphs 5.21 and 5.22
I am very sorry I cannot be at the meeting on 16 November, but I fully support your efforts to keep the library open. Another gym is not needed: people who want a gym are sufficiently mobile to use gyms farther afield, people who need the library – young or old- quite probably aren’t. The proposal is not an acceptable substitute