I would suggest that you first discuss with the local authority the issues and concerns they have regarding linking in the their library management system.
There are huge benefits to integrating with the Local Authorities system, and this is likely to enable you to offer a much better service for your users.
There are some challenges for authorities to deal with, which will vary depending on the particular system they use. They may for example have concerns around data protection or security, or cost implications for changing their system.
Another example of how to start, with a pop up co-working library lab!...
http://www.cles.org.uk/features/the-library-lab/
Also see Meanwhile Space http://www.meanwhilespace.com/