No, not really, it's the same way that C compilers are written in C. The first one was written in another language like assembly, to be sure, but after that you could use the first compiler to write a second compiler in C, and the second one to write a third one, and so on.
In this case, I'm assuming the first version of the compiler was written in Javascript. After that, they could use the first Javascript-based Litescript compiler to compile a Litescript version of the compiler, and once you have that you never have to go back to Javascript again.
Cool, I did think it might be that, but when I read "LiteScript is written in LiteScript, every new version must be able to compile itself to be ready for release" it just kinda makes it sound like some kind of magic is happening, where a version of the language, before even being compiled, can somehow compile itself in some super clever way that I was just missing.
In this case, I'm assuming the first version of the compiler was written in Javascript. After that, they could use the first Javascript-based Litescript compiler to compile a Litescript version of the compiler, and once you have that you never have to go back to Javascript again.