The Driver benefited greatly from it. As he cultivated with Lan Jue, most of the thunder essence's energy was absorbed into Lan Jue's body. However, even in ancient times, thunder essence was a top-notch treasure. The Driver had absorbed a small portion of it, which was enough to lay the foundation for him to become a Paragon in the future. It also allowed him to truly find his own path.
Lan Jue's cultivation did not increase much, because he was deliberately suppressing the speed of his improvement. Instead, he was trying to purify and forge his energy as much as possible.