My apologies. I actually received an email of the Lexus Spain press release announcing this a week ago but forgot to spread the word. Said release ( https://estilolexus.lexusauto.es/espacio-lexus-en-el-aeropuerto-de-madrid/ ) refers to it, in colorfully bilingual manner, as Espacio by Lexus. Though not spelled out in so many words, my suspicion is that this is a first attempt to make smaller, pop-up store "Space by Lexus" (or "Lexus Space") counterparts to the larger, fixed Intersect by Lexus venues. Indeed, the Spanish news release refers to it as "Pop Up Store by Lexus – Barajas" at one point.
Other tidbits in the news release are that the mini-lounge features its own dedicated free Wi-Fi, furnishings echo those found in Lexus' European dealerships and that the winding bookcase/paneling/shelving is made of bamboo wood.
One final, somewhat enigmatic bit: Lexus Spain is holding a contest where if you upload photos of the Madrid-Barajas Espacio by Lexus with #LexusLCBarajas, tagged to Lexus España, you can win a "Lexus-branded helmet" (!?) My best guess is that it's the Sparco racing helmet that appears in the Boutique Lexus España page ( https://www.lexusauto.es/lexus-today/boutique-lexus/#Introduction )