Same old story. You all want the same, or better, LA services out of a diminishing pot of money, but you're not willing to pay more. This is the real world.
For money to get through to support libraries (or social work, road maintenance, housing or any other arguably more important LA service) requires firstly a bigger settlement from the Govt to the LA and only then a reallocation of budgets within the LA. Even if a LA successfully negotiates a larger share of Govt money, there are no guarantees that keeping libraries open would be top of the list.