For more than two decades, the K-pop industry was dominated by the trio until BTS rose to global fame in recent years, making its agency HYBE the largest music label in the country.
It is the second-largest entertainment group in South Korea by market value at $2.8 billion, trailing HYBE, which is worth $5.5 billion.
Lee filed an injunction request to block the deal that was approved by a court, and sold a 15% stake in SM to rival agency HYBE, setting up a takeover battle.
Kakao, the most popular social media platform in South Korea, is expanding aggressively into the entertainment industry where it already owns a smaller K-pop agency, Starship Entertainment.
In January, Kakao Entertainment announced a 1.2 trillion won ($966.27 million) investment from Singapore's GIC and Saudi Arabia's Public Investment Fund, giving it more firepower for the SM bid.