It's not a wholly conflicting point underneath. What's the point of trying to do anything with LCC as a focus in a context where both they and all the structures above can point at the constituents and say that, well, they democratically chose austerity as part of the national plan?
At least if you take that as a given, and decide to persist at council level, at the most simplistic level there's two options. Do something unilaterally, win and be able to demonstrate popular support through that. Or change the fundamental support first and persuade the constituents to express a new message at the ballot, then act on it. And both times we're into the nature of what the Lancashire demographic is.
Or you forget the council, treat it as an outcome rather than a factor, and go after the national imbalance, as many are - why London & the SE on the whole don't face such austerity.
Can any of that be done via Labour, I've no idea - and don't enormously care either way, tbh. Some of the above lends itself to Labour more than others, some is probably impossible with it as it stands. If it were a functioning, unified movement it might help.