From my understanding; Lange & Sohne distribution is in the New York/New Jersey area, this is the sole distribution facility for all of North America, Central America, and South America.
Their distribution facility in New York/New Jersey area is not very large and doesn't necessarily stock pieces. I imagine that because of this, they actually have to wait until they have large enough quantity order before they go to Germany and order a couple pieces. Or, maybe they make orders on a schedule of every two months. I don't know, but I think this is a reasonable assumption.
This is my assumption of how the system works. I heard this information from another Lange lover in late 2008 and since then I've heard small tidbits here and there that corroborate this story. However, the distribution system may have changed by now.
Thus, if the aforementioned is true, then it would make sense if it takes your watch 2-3 months to order. Keep in mind, your dealer may be underpromising and thus giving you a very conservative estimate.
Looking forward to hearing about your new Lange watch soon!