I used both VS2013 and VS2015 now, all of the vcvarsall.bat targets ("x86" and "amd64_x86") that can produce x86, result in that error.
Also, do I have to use a x86 JDK to build the natives? I mean I did now and their header files are identical.
Hmm... strange.
EDIT: Thank you for the hint with the x86 JDK. Now that I actually DID use a x86 JDK in JAVA_HOME when calling ant (not just in PATH) it now works. But why....?

EDIT2: Ah... I think I know why now. Because the LWJGL build process builds the architecture of the LWJGL library based on the identified JDK architecture running ant. And if that does not fit the VS build/arch, BOOM.
