The $350,000 Lexus LFA was one of the most buzz-generating vehicles at the ultra-luxury "Gallery" exhibit during the North American International Auto Show in Detroit this week. Coined the "two-seat supercar" by Lexus, the vehicle sits at the top of Lexus's "F" portfolio, its line of high-end sports performance vehicles.

But simply having the $350,000 to buy one of the 500 LFAs Lexus plans to produce won't be enough: Buyers must be tapped by the company to be owners. People selected to purchase the car will be based on factors...