According to local news agency Yonhap, the LPX-II project aims to build a new versatile large-deck landing ship for short take-off and vertical landing fighter jets.

F-35B STOVL fighter capability
HHI is expected to finish the conceptual design by the second half of 2020, with commissioning with Republic of Korea Navy planned for the early 2030s. The vessel, displacing around 30,000 tons would be based on the existing Dokdo-class amphibious assault ship (LPX-I project) and would be able to accommodate around 20 F-35B STOVL fighters.

The LPX-II vessel will also deploy future Marine Attack Helicopters of the ROK Marine Corps, for which there is an upcoming competition between local company KAI (with the Surion MAH), Bell Helicopters (with the AH-1Z) and Boeing (with the AH-64 Apache). All three companies were showcasing their solutions at ADEX 2019. As ship to shore connectors it will likely deploy the future KAAV-II as well, for the which the design was unveiled at the air show.
Earlier this month, HHI won an initial production contract for the KDX III Batch II, the next generation of AEGIS destroyer for the ROK Navy.
Talking to Naval News during the Seoul Airshow (ADEX 2019), Lockheed Martin representatives said they could not comment about potential F-35B procurement by South Korea.