How to plan a project with Lean UX?

I have to make a ux de proposal for a project that already exists. For which I have decided to do it with the Lean UX methodology. I am new to implementing this methodology and I needed you to help me plan the tools to use in each of the three phases (Think, make and check).

It is for a small project and I would like the company to invest more in the UX department through this project.

Thanks ;)