Final answer:
The supply road built in the 1930s and used during World War II from Lashio to Kunming is the Burma Road.
Step-by-step explanation:
The World War II supply road with a "national" name built in the 1930s, stretching from Lashio to Kunming, is known as the Burma Road. This road served as a critical supply line for China during World War II after Japan's blockade of the Chinese coast and occupation of Vietnam. Unlike the ancient and mythical Silk Road, which was a network of trade routes, the Burma Road was designed for modern vehicular traffic to ensure the steady flow of goods essential for the war effort.