Every type of project management, if well applied, ought to lead to a “Lean” situation.
My 2 ps: Lean is more a “brand” than everything else.
By the way, I do not like the Toyota system; the reasons why it is so are explained in this article.
As for Agile, it is SW-tailored; in my opinion, its use is abused, for Agile should be operated together with a traditional project management methodology: on one hand, you have the day-by-day work (Agile), on the other hand you have the general management (traditional methodology).
Waterfall is the traditional way of producing SW: one step after the other. In the end, every project is (and must be, otherwise how could you apply managerial controls and checks?) waterfall, but it can include parallel activities, SW modules, and so on.