When I saw the Trilogy what stood out for me that was so Indian was the battle scenes. In one battle scene, they ride out to meet the Orcs in a final show of force. It was so vivid from the annals of Rajasthan where the Rajput Kings would ride out to meet an ocean of Mughal soldiers.
I remember telling this to my friends several times. Unlike the movie version, the real history was far worse. Before the Rajput Kings rode out to their doom the Queens, the Royal family and all the Women and children would dress up in their wedding dresses or the best attire, sing Hindu Hymns and walk into a giant pyre. At the Rajput Fortress of Chitor over 36 thousand women and children committed Jauhar. It was repeated twice. At another Fortress, over 12 thousand committed Jauhar.
The next day the Kings would anoint themselves with ashes of their loved ones, take Opium to kill any pain and then ride out to their doom. Mughal Armies seldom took prisoners. They would kill anything that moved after they took over the Fortress. Women were violated and then killed.
Usually, one Prince is smuggled through secret tunnels deep into the mountains so that he will grow up and reclaim the Fortress, which often happened. that was also present in the Trilogy where the people of the Kingdom of Rohan hid inside a mountain. In Sri Lanka, there was the Kingdom of Rohana. Again that name rang a bell with me. I am from Sri Lanka.
The Ents are so Hindu I could not shake it off. All of Hinduism, Buddhism, and Jainism believe that trees have living spirits called Yakshis. Yakshis are found profusely carved on Temples and Buddhist Viharas. The Forests are alive.
Of course, the war elephants seem to come straight out of India.
On another note, in Star Wars there is a system called the Dagobah system. I wasn't aware of it till I wrote up an article on Sri Lanka and her ancient "Dagobahs" which are some of the largest ancient monuments ever created. The Jetevaranama Dagoba is 400 feet and only shorter than the tallest Pyramid of Ghiza. At 93 million bricks it is still the largest Brick structure in the world.