You mentioned that it "comes with the box (the long one)." Can you post a picture of that inner leather long box in an open position? Also, can you provide the first 3 digits of the caseback serial number?
Lange changed its box style in the early 2000s, but the original box for this watch should not be long and rectangular. It should be a square box, and the black leather inner box (with cream interior) should have a single brass latch. There should also be an outer cardboard box (blue/gray color) and an outer cardboard sleeve (same color) that fit snugly around the inner box. That inner square box looked something like this:
[If you're interested ... The size of the original (almost) square box would have depended upon when the watch was made: The very first boxes were smaller because the only papers were a small paper warranty card and a small instruction booklet, which both fit inside the inner box below the watch holder, which lifts up. Shortly after Richemont acquired Lange, Lange introduced a black leather wallet to hold the papers. That black leather wallet rested above the black leather inner box, and so the combination required a slightly larger (taller) outer cardboard box and sleeve -- and the watch older was no longer removable because nothing was stored beneath it.]
When you say it comes with the "long" box, two long, skinny boxes come to mind. The first is a long, skinny leather box with no brass latches. That box, with no brass latches, originally came with the old 1815s (which were the least expensive Langes at that time). Here is a pic of that box:
The pouch inside the lid of this box held the papers. Lange used the larger square box with one brass latch for the "middle-range" models such as these Langematiks and the Lange 1, and Lange used an even larger box with 2 brass latches for the "highest-range" models such as the Datograph and the Tourbillon Pour Le Merite.
The second long box that comes to mind is a Lange service box, which is a long, skinny cardboard box with grey foam inside and no leather anywhere. Lange uses them to ship watches back to customers and dealers after servicing. This photo shows the difference between the box just above (old 1815 box) and the service box:
This sounds like a watch that comes with no original boxes or papers, which is totally fine as long as that is reflected in the price. The "Proof of Origin" from Lange is nice to have, but as Mahesh says, I would still contact Lange with the full caseback serial number just to confirm that it wasn't stolen in the past year.
Congrats and good luck with it, if you go through with it -- and please do post pics of the box if you get a chance!
[I realized that this is FAR more than you wanted to know and that you might care about right now -- that you're just trying to figure out whether all is okay with this pending purchase. I'm just adding the details for general interest/knowledge.]