Kim, Khloe and Kourtney Kardashian Sued Over Beauty Line

Kim, Khloe, and Kourtney could be on the hook for more than $200 million for not tweeting about their own makeup line ... this according to a new lawsuit.

Hillair Capital Management claims it ponied up more than $10 million to save the Kardashian sisters' struggling cosmetics line, "Kardashian Beauty" ... after their former business partner went belly up.

As we previously reported, the Kardashians originally partnered up with a company called Boldface in 2012, launching a makeup line called "Khroma Beauty."

Problem was ... a year later, a judge blocked the company from using the name "Khroma." The girls changed the name to "Kardashian Beauty," but Boldface started tanking.

A savior stepped in ... Hillair Capital Management, buying out Boldface and sinking $10 mil into the business.

Hillair now claims the Kardashian girls didn't hold up their end of the bargain by blasting out the virtues of "Kardashian Beauty" to their millions of followers.