Lua installation fails: String.h file not found on macOS Mojave

[Harald von der Osten <hvdosten@...>]

Xcode and command line tools are installed, and

"xcode-select —install“  gives me "xcode-select: error: command line tools are already installed, use "Software Update" to install updates“

and "softwareupdate --install Xcode" results in:

 "Software Update Tool

Xcode: No such update

No updates are available."

But when I try to install Lua using  "make macosx test“ the error message „string.h: No such file“ 

/Library/Developer/CommandLineTools/usr/bin/make all SYSCFLAGS="-DLUA_USE_MACOSX" SYSLIBS="-lreadline"

gcc -std=gnu99 -O2 -Wall -Wextra -DLUA_COMPAT_5_2 -DLUA_USE_MACOSX    -c -o lapi.o lapi.c

lapi.c:14:10: schwerwiegender Fehler: string.h: No such file or directory

 #include <string.h>

          ^~~~~~~~~~

Kompilierung beendet.

make[1]: *** [lapi.o] Error 1

make: *** [macosx] Error 2

Where can I find the correct string.h file? And into which subdirectory must it be copied?

Thanks a lot.

Harald