If you have "make" (a standard build automation tool in Unix-like systems), "cpp" (the C preprocessor - most Linux distribution probably have it as a separate package, you will also automatically get it as a dependency when installing the "gcc" C compiler), gregorio and LuaLaTeX, the only command you need to execute is "make", which reads Makefile and executes the command sequence specified there. I.e. you don't "run make with latex", but rather "make" runs latex (and everything else needed to build the document, as specified in the Makefile) for you.
If you wanted to execute the command sequence without make, it would be as follows.
# 1. process C preprocessor directives, produce pure gabc
cpp -P salva_nos.gabc.cpp > salva_nos.gabc
cpp -P -DTEMPORE_PASCHALI salva_nos.gabc.cpp > salva_nos_paschal.gabc
cpp -P responsory.gabc.cpp > responsory.gabc
# 2. build the LaTeX document