All four Indians, who made the cut were inconsistent.
Madappa, who shot 69 in third round and raised visions of a top-10, collapsed with an 80 and Chinappa, who carded 73 on third round, carded 76. Both finished at 301.
Karan Taunk (80-78-68-76) and Udayan Mane (80-77-72-73) totalled 302 and ended tied 39th.
Manu Gandas (83-77) and Syed Saqib Ahmed (80-82) failed to make the cut.
Lee fired a closing 70 for a 3-under-par total that earned him an invitation to next year's Masters Tournament. He also secured a place in International Final Qualifying for The Open Championship along with runner-up Shohei Hasegawa of Japan, who shot a 71.
Hasegawa's compatriot Kenta Konishi (70) finished strongly to claim solo third place at 1-over.
After posting earlier rounds of 70, 72 and 69, Lee started the final day with a slender one-shot advantage over 16-year-old Dou Zecheng, who was looking to become the second Chinese player to win the championship after Guan Tianlang's victory in Bangkok 12 months ago.
Lee, 19, became the second Korean to win the championship after Han Chang-won claimed the inaugural event in 2009 at Mission Hills Golf Club in southern China.
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