That's not true at all. Learning how to program is more or less about learning the logic of how a code operates, what is OOP and how it works, what are the general programming practices and small things like that. Second comes the knowledge of what your platform/environment is capable off - what can the Warcraft 3 engine do, what causes it to desync?
A deeper knowledge of your chosen language is only tertiary. After having the first two, learning a new language is a piece of cake. Obviously, you learn the first two while learning a language, but it can be anything. Hell, GUI and Garry's Mod's E2 programming taught me the basics that helped me get a grasp on how it works.
Even more so, JASS operates quite similarly to C++ and C in some regards - you don't have a huge and comfy safety net like .NET under you: no massive pre-written and pre-compiled functions, no garbage collector to remove your leftover references.
LUA is a pretty simple scripting language, and I'd probably go at it through modding some game and look up the specific tutorials.
I don't see the point of learning C, since C++ is superior to it in basically everything that's not embedded system programming (in which case it's C or Assembly), and if you want to write any kind of programs for desktop/smartphones, you better go with C++. There should be quite a few books for that both in stores and on the net, and for C++, you can start with
the official tutorial for C++, but
this one look quite good as well.
Also, I like that LUA learning game.