In my experience agile development can be antagonistic towards UX, especially if UX is attempted to be made to fit within an agile development frame work. The issues with agile don't relate to how successful then can be for development teams but when either UX concepting is attempted within sprints or if key design is done on the fly with the development driving the design. Agile is great for developers and UX, in my experience, works best when it feeds that development process with the right level of specification for what is being built.
And that is where Lean UX comes in. From my understanding (and different people understand it differently), Lean UX is all about reducing the amount of deliverables and attempting to create what is needed to concept, communicate, test and develop the final UX. What is 'right' differs between projects and, most importantly, between the team you have. No one process is right for all teams and all projects and it is the team that, ultimately, makes the project work or fail, not the process.
Lean UX also taps into an old idea of trying to make designers view all team members as collaborators on the design. A good development team will work well with their UX resource and a good UX team/person will ensure that developers are involved with the design process. Having said that the important part is that the UX effort is respected and that the developers are given the permission to focus on engineering and implementation and are not responsible for design or functionality.
Lean UX works best when a production line is working where UX solutions are delivered to the developers when they needed but the developers only have the responsibility of saying when UX solutions are not feasible.
So, in summary, Lean UX, if done well, is a great complimentary approach that fits in well with an Agile development team, but it's not really the same thing.
Also Lean UX is not the same as Lean Start up as it does not have to build then test but can spend time researching how users use thing, providing it's done in a light way, for example two weeks spent interviewing staff members about an intranet is great whilst a two month research process is not Lean.