Is Agile a subset of Lean?

Is Agile a subset of Lean?

In my opinion, no.

Lean and Agile go hand in hand, in my view, but are no subset of each other.

Both Agile and Lean support the "just in time" delivery of a working product (increment) and maximizing value. So this is a theme that is common with both. But they focus on different aspects on how to achieve this.

Lean focuses on optimizing the flow of work. Minimizing waste and limiting the Work in Progress.

These concepts work well with working Agile; minimizing waste as in not refining or not refining into too much detail of PBIs untill needed. Or minimizing waste as in technical debt, manual testing, dependencies. Minimizing waste in people waiting on each other, not working effectively.

Agile focuses on innovation, taking into account empirical data and short feedback loops to maximize the value delivered. The more clean the process, the more Transparency, which helps the Inspect & Adapt pillars of Scrum.

Scrum also focuses on continuously Inspecting and Adapting, and therefore continuously improving. This is also one of the common areas between lean and Agile

So in my view, Lean principles and Agile principles enforce and help each other. Take Lean concepts and combine these with an Agile way of working, and you get a combination as a "best of both worlds" scenario.

That is what Lean-Agile is to me. Always Inspect and Adapt what value we are delivering and how we are delivering it. Continuous Improvement. Optimizing the flow (process), limiting waste in all concepts where possible, embrace all the concepts of the Agile Manifesto and Scrum framework along the way

First, I point out the agile is an adjective. Google "agile definition" and the first statement is 

1. able to move quickly and easily.

Lean was a manufacturing process created for the purpose of eliminating waste in the process of creating a product. 

They are complimentary to each other.  Combine my statements and you get 

Eliminate waste in the process of creating a product while being able to move quickly and easily. 

My question stemmed from this article.

https://miro.com/blog/choose-between-agile-lean-scrum-kanban/

Scroll down and look for the diagram.

Let me know your thoughts.

I read the article you referred to.  Honestly I did not see anything to indicate that agile is a subset of Lean. Even the article states that they are different. I see the chart you referred to, I see the statement just before it that says agile is a subset of Lean.  But that it the opinion of the person that wrote that article and the people that wrote the articles he references.  As with all things on the internet, look long enough you can find things to support your own opinion and theories.

I want to point out one thing about that article that sort of rubbed me wrong from the beginning.  Agile, Lean, Scrum, Kanban are not methodologies.  From Merriam-Webster I pull these two definitions

Methodology - a body of methods, rules, and postulates employed by a discipline : a particular procedure or set of procedures

Framework - 

a: a basic conceptional structure (as of ideas)

b: a skeletal, openwork, or structural frame.

Scrum and Kanban provide a structure that has been shown to be effective with some guidance in the way of elements. Lean and agile provide a basic concept of ideas that can shape an organization to be more efficient and effective.

Now to prove my point, see how I was able to find information on the web to support my opinion?  Read articles, books and whitepapers but use them as sources to expand your knowledge, not as descriptions of what is "right".