Well for one there is many different compounds for batteries than just lithium manganese, secondly since lithium exists as a mineral in nature it is relatively easy to process into different salts and compounds and to purify. You make it sound as if the Chinese have pre-made lithium manganese oxide just oozing from the ground without the need of processing. Well I hate to burst your bubble, thats not how they do it. They extract the lithium from lithium carbonate deposits and then create the compounds for Li-ion batteries from that.
You need to read up on this. You do know that manganese is an element, not a process, right? And that lithium manganese dioxide is a mineral not the result of processing lithium. If your contention is that lithium deposits can be commercially synthesized into lithium manganese dioxide, you are just wrong.