It's surprising to think that Koreans buy almost as many premium cars as the Japanese. About 250,000 are sold each year although Lexus isn't the biggest as you might expect. If we first look at premium marques minus the big three, Lexus is indeed the main make with over half the total sales. However 2017 wasn't too kind with sales down 6,500.
In the charts below, the % in the aqua line is comparing sales to the previous year, but otherwise it is the share the brand has of the total.
Now taking all the above registrations and combining them into 'Others' below, the above marques are the largest contributor but not by much. BMW is greatly aided by a very popular MINI, which is nearly as successful as the whole Audi range.
Data source: JAMA, JAIA.