First, Lange used to accommodate many special requests (such as the hand color change in Luc's watch). That makes it difficult to determine whether a watch actually left the factory in its current condition, or whether Lange changed a dial, hands, etc., later.
Second, Lange's early reference number system was somewhat random and inconsistent. The Tourbillon "Pour Le Merite" series illustrates this nicely: Supposedly the only difference between ref. no. 701.001 and 701.002 was the strap color!
Third, Lange had some sort of computer system switchover around the
year 2000 -- maybe around the time Richemont stepped in -- and that
switchover apparently makes it difficult for Lange to cross-reference
information for early watches. If you can provide Lange with a specific caseback number, then I believe they can look up that caseback number and tell you
the reference number with certainty. But if you don't have the caseback
number -- if you have only a photograph of the dial -- then they often
can't tell you the reference number with certainty. They can offer only a
best guess, which is usually (but not always) correct. The piece that
you referenced, vs. Luc's watch, illustrates this: They are identical in appearance, but one has a warranty card that says
403.025 (it pre-dated the "Pisa" series), and the other has 403.025X because it was part of the "Pisa"
series but had a "custom" second hand in rhodium rather than blue steel.