It's the most unlikely pairing in any lawsuit ever -- Justin Bieber and Eminem -- but believe it ... because they're at the center of a new legal war over a concert in Korea ... that will never happen.

A company called Moonstone Management just filed a lawsuit in L.A. County Superior Court -- claiming it hired another company named J-Mike in 2010 to recruit either Eminem OR Bieber for a concert in Seoul, Korea ... and J-Mike never delivered.

According to the lawsuit, Moonstone paid J-Mike a down payment of $300,000 to secure one of the stars -- but J-Mike strung them along for months with nothing to show for it ... and eventually called off the deal without returning the cash.