Could you describe the specific ritual Sai Baba performed with the water and the tiny bit of oil before lighting the lamps?

Yes, Chapter 5 details the precise and symbolic actions Baba took. After being refused oil, he returned to the mosque where his tin pot had a very small amount of oil left. Instead of trying to use it directly, he first poured water into the pot with the oil. Then, in a significant act, he drank this mixture himself, making it an offering to Brahman (the Supreme). Only after this ritual of consecration did he take plain water and pour that into the lamps, soaking the dry wicks completely. He then lit them, demonstrating that the power to create light came not from the oil, but from a higher source.