I asked about the book sharing concept at the newgenlib mailing list.  Here
is their response:

We would like to first appreciate this innovative concept of lending
> library.
> As you have mentioned for this concept we either need to implement an ILL
> or Network library to realize this.
> ILL is available in NGL in Circulation functionality.
> However from a "traditional" library's point of view an item loaned on ILL
> basis is usually meant for one patron only. Once the patron is done with the
> item it is returned back to the lending library. Which is not your case!
> Using Library network will be heavy weight.
> Also, most of the books in a library are its own property, hence accession
> numbers are provided for them.
>
> As of now NewGenLib does not meet the  such requirements. We will consider
> this business case in our next development cycle.
>

I expect any other ILS not designed for book sharing would have the same
limitations in their ILL system.