The original LCM24064YGF LCD was stuck on the display shown below.
Despite considerable effort, attempts at finding information on the LCM24064YGF display proved unsuccessful.
Though 240 x 64 pixel displays are relatively inexpensive and readily available, the are two issues which render replacement problematic:
The vast majority of 240 x 64 pixel LCD modules currently available, have an integrated controller chip. The image below shows such a controller for comparison with the LCM24064YGF. Though both designs include XY drivers, the LCM24064YGF clearly lacks a controller. In the case of the latter, the controller, an M66271FP, resides on the Z1's main board.
Controller-less LCD modules are still available in theory, but finding an actual supplier is a different matter. For example: The BOLYMIN BG24064D is controller-less and seems like it might work with the M66271FP controller. The module is available from Alibaba.com, but has a minimum order requirement of 500 units.
Even if such a module could be procured, and even if it does work with the Z1s controller, there remains the problem of fitting it inside the Z1.
The LCM24064YGF measures 166mm x 55mm.
The display mounting cavity in the Z1 closely mirrors these dimensions, especially height wise, where two metal walls rigidly enforce the 55 mm restriction.
The width limitation is slightly less rigid, but not by much.