Star Trek works in mysterious ways:)

Well, they do share the word “lithium” for sure.

Rags can correct me if I’m wrong but my understanding is that the power actually came from matter antimatter reaction and the dilithium was used to focus the energy into a usable power source. But it’s all mythology and it’s whatever the writers thought at the time. Anything else is retconning.

Chemistry and the names of compounds have been know long before Gene Roddenberry was a glimmer in a test tube.