If you're spending the first night in Tokyo, you can use something like bikeflights, ship the bikes to your hotel a few days in advance. It just takes a bit of coordination, but folks do it all the time.

However, before doing anything complicated, I'd speak to Lufthansa. The planes they fly on these routes are large and have plenty of excess baggage capacity so I suspect someone might be giving bad info. Alternatively, do as I do, and break the bike down so you can pack it in two bags, one for wheels, one for frame, with the rest wherever it fits. I do this and use my clothing as padding, with some EP foam as protection all the way around. I pack in two large duffels because the airlines don't measure those too precisely, and when I check in, it looks like I have 2 hockey or diving bags, and nobody says Boo.