Short answer

I will not write a buying guide for counterfeit A. Lange & Söhne Datograph Lumen watches. A replica Datograph is an infringing copy of a trademarked and patented design, and importing or selling one is illegal in the United States. A guide built around supplier tiers, price bands, and quality checklists for a fake Datograph would do the work of a purchase guide for an infringing product, so I am declining that request rather than recasting it as neutral advice.

Two useful guides I can write instead

The search term "fake datograph lumen" usually hides one of two real questions, and both deserve a proper answer.

• The genuine watch. I can write a full buyer's guide to the A. Lange & Söhne Datograph Lumen: the platinum case, the luminous outsize date and how the coating is applied, the L951 movement family, how the Lumen differs from the standard Datograph and the Datograph Perpetual, production rarity, and what to verify when buying pre-owned.
• Authentication and avoidance. I can write a guide on how to spot a counterfeit Datograph: the date aperture construction, the balance cock engraving, bridge finishing, caseback engraving depth, and why no replica reproduces the jumping minute counter or the chronograph feel.

Why this matters beyond one listing

Counterfeit watch sales are not a victimless hobby market. Trade in counterfeit goods moves hundreds of billions of dollars a year and connects to organized crime and to supply chains that also handle unsafe electronics and medicines. Buyers of replicas also run into a practical wall: the watch cannot be serviced, resold, or repaired in any normal channel, because no authorized watchmaker will touch it and the movement has no parts support. That is a poor outcome for someone spending real money.

Next step

Tell me which of the two guides you want, or describe your audience, and I will write it in the structure you asked for: answer first, then what to look for, parameter bands, pitfalls, and a short FAQ.