Lamborghini sells under 2500 a year.
Chalk this article up to careless punditry, i.e. what you get from an ad-driven internet news model.
Edit: just for kicks, I looked up Rolls Royce, which is kind of the canonical "luxury car". Under 4000 cars a year.
All of these cars use technologies funded by or borrowed from their parent. Lamborghini was seriously behind the cutting-edge when VW bought it, now they are catching up (last independently made Lambos had tubular frames).
One of the smallest independent automaker is Mazda, it produces around 1.2M cars per year, they can afford this because they're really innovative.
Tesla has some leeway for now as electric engines are significantly simpler than modern combustion engines, as the latter are extremely difficult to design because of environmental regulations (especially European ones). Designing a nice interior or rigid chassis is simpler than operating a naturally aspirated V10 in the E90 M5 that has an Euro5 cert..
Lamborghini belongs to Volkswagen (as do Bentley, Bugatti and Porsche).
Rolls Royce belongs to BMW.
None of these except for Porsche were viable on their own. At the very least, they need R&D for engines and other components from their parent, but usually much more.
In many cases, they are viewed more as a branding exercise by their parent companies, somewhat like luxury brands like the Phaeton (VW) or Maybach (Mercedes), which are also usually not profitable.