How does Design Thinking, Agile and Lean UX work together?

I have become confused on the different processes involved between Design Thinking, Agile and UX Lean.

I recently read an article that tried to explain how these processes work together as I wanted to check if I have understood these correctly.

The article stated that a UI/UX designer will first run through their process of Design thinking, in order to provide the developers the correct information to build. For example a website. Once the developers start to build, they will follow a agile process, building aspects of the project in stages/sprints.

The results of these sprints are then further tested and feedback is given to the developers to implement, which is how the UI/UX designer is then part of the Agile process.

Is this correct? If so, how does Lean UX fall into this explanation?