was lost, is in China. do you mean Outer Mongolia? Is it lost? I would think Japanese are Chinese who seperated from China way earlier than most others.
A story of a minister under Qin Shi Huang, went East to fetch longevity elixir with selected 400 male and 400 female Chinese comes to my mind on the Japanese's origin. I also heard today's Japanese dress and language are or at least Closely resemble those of Qin Dynasty. They are quite conservative, having change very little, that helps to easier identify them. They, will most likely, not agree to such statement now and keep insisting they came from Sun God as their legend says.