You are right of course, and the lathe is turning too fast anyway. The way I do it is to use the lathe only to hold the die and the piece inline. The lather is stopped when i cut the thread.
For the die I have this holder that freely spins on a shaft. The shaft goes in the drill chuck - or you can have MT2 on it, same thing. See the picture, it is better than my clumsy english.
I use it to thread gun barrels, the alignment there is much more important than bike axle thread

Not my idea, found it here -
http://bbs.homeshopmachinist.net/