This question is one I've run into a few times recently. It's not a question I can answer quickly as the question is based on a false premise about the relationship between lean and agile. So first I need to go into some history to help explain that relationship.
"Lean" fundamentally refers an approach in the manufacturing world that was originally developed by Toyota in the 1950's. At this time Japanese industry was recovering from the ravages of the second world war. This approach, often called the Toyota Production System is mostly credited to Taiichi Ohno, although he was influenced by various western thinkers - particularly Deming. The Toyota Production System became well known in the rest of the world in the 1990's when westerners started writing books to explain why the Japanese were beating the US at so many industries. The western writers called this approach Lean Manufacturing. Although Japanese industry in general has run into stickier times since then, Toyota continues to outperform most western auto companies.
Agile software development is an umbrella term for several software development methods (including Extreme Programming and Scrum) that were developed in the 1990s. These methods share a common philosophy which was described as values and principles in the Manifesto for Agile Software Development. (My essay "The New Methodology" goes into this in more depth.)
There was a connection between lean manufacturing and agile software from the beginning in that many of the developers of the various agile methods were influenced by the ideas of lean manufacturing. This connection was made more explicit by Mary and Tom Poppendieck. Mary had worked in a manufacturing plant that had adopted lean manufacturing and her husband Tom is an experienced software developer. They have written a couple of books on the application of Lean ideas in the software world. When people talk about Lean Software they are usually referring to the ideas in these books, although others have been making similar links.
Lean manufacturing and agile software methods have a very similar philosophy. Both place a lot of stress on adaptive planning and a people focused approach. As a result lean's ideas fit in very well with the agile software story. Mary and Tom have both been very active in the agile community - indeed I'd credit Mary with an important role in forming the Agile Alliance. (Like me, she was a founding board member of the Agile Alliance, but she was far more effective in it than I was.)
I've already mentioned that lean manufacturing was an influence on agilists from the beginning, and in the last few years more ideas have appeared in the agile world with a clear lean manufacturing heritage. These range from concrete techniques like Value Stream Maps, to articulations of existing agile concepts such as the Last Responsible Moment for making design decisions. The idea of thinking of analysis and design documentation as inventory came from the Poppendiecks. Several agilists I know emphasize the importance of reducing cycle time - another strongly lean-influenced idea. My colleague Richard Durnall has a nice summary of how lean knowledge can blend in with agile thinking.
A particularly strong appeal to many people about lean ideas is that they provide a way of explaining agile software development to people - particularly senior people both within IT and senior customers. This explanation ranges from a crude appeal to emulate Toyota to detailed discussions of how lean manufacturing's benefits translate to the ideas in agile software development.
So as you can see, lean and agile are deeply intertwined in the software world. You can't really talk about them being alternatives, if you are doing agile you are doing lean and vice-versa. Agile was always meant as a very broad concept, a core set of values and principles that was shared by processes that look superficially different. You don't do agile or lean you do agile and lean. The only question is how explicitly you use ideas that draw directly from lean manufacturing.
The Poppendiecks didn't introduce lean as a separate idea, nor did they introduce lean as a published process in the style of Scrum or XP. Rather they introduced lean as a set of thinking tools that could easily blend in with any agile approach. I think of lean as a strand of thinking within the agile community, like a pattern in a rich carpet.
There is a distinct lean software community, as in a mailing list calling itself lean and people who label themselves as lean thinkers. But this is no different to the fact that there are also strong XP, Scrum, and other communities. Most people in these communities consider themselves part of the broader agile movement and many people are active in more than one of these agile communities. The whole point of coining the word 'agile' comes from a recognition that we share a core set of values and principles and this common core means what we have in common is greater than our differences.