SUZHOU, China—A new cancer drug licensed by Eli Lilly & Co. was discovered by a six-year-old startup on the outskirts of Shanghai, and derived from the ovary cells of Chinese hamsters. Lilly now is planning to test it on Americans.

Rival Merck & Co. aims to test a separate cancer drug in the U.S. this year, created by another startup near the border with Hong Kong.

Those...