I'm basically familiar with Agile methodology and Scrum.
But what is "Lean Software Development" and "Kanban"?
Is it safe to say that Scrum, Lean and Kanban are implementations of Agile methodology? Or are Lean and Kanban different methodologies?
Do Lean and Kanban provide a skeleton/guideline (like Agile) and leave the implementation to an adjacent set of practices, like XP and Scrum?
Agile expert Mary Poppendieck wrote about the principles of Lean. Find her credentials here.
Instead of me writing a lot about Kanban, please read what Swedish advisors Crisp say about it.
The practices of Lean are quite different from the hands-on, practical tasks that programming-centric XP asks you to do in your project ("Automate everything", "Have tests", "Meet daily"). Value-stream analysis could give you some new insights and conceptual tools with which to reason about business and tasks to do.
Hope this helps navigating the process-speak. Best of luck!