Compatibility of an LCD module and a connector
The connector on LCD module is FPC, which is "flexible printed circuit". It is possible, although quite cumbersome, to solder FFC (flat flex cable) to FPC. However the end result will be fragile and FPC can be damaged with time.

I would suggest making PCB board with 12 pads 0.5mm wide, spaced 0.3mm apart. The pads will spread to 0.1" holes which you can use either to solder that cable or to populate with pin header to be mated with the header on the cable. Something similar to this but with single row of 12 holes:



Ideally the PCB should be big enough so it can be attached to the back of LCD with thick and soft double-sided mounting tape. This will minimize strain on FPC.

UPDATE

Actually, digikey has suitable board in their catalog, but no inventory available. Here it is directly from proto-advantage