Try LDDLFLAGS.   As it defaults to $Config{lddlflags} (i.e. perl -V:lddlflags), you have to be careful not to overwrite anything that might be in there already (in other words, whatever you specify does replace, not add/append to it).

As a last resort, you could try OTHERLDFLAGS (which is typically unused). — Usage (in Makefile.PL):

WriteMakefile(
    ...
    dynamic_lib => { 
        OTHERLDFLAGS => "-Wl,-rpath,/your/lib/path"
    },
);
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(In the link command in the Makefile, the values are issued in the following order: $(LD) $(LDDLFLAGS) $(LDFROM) $(OTHERLDFLAGS) -o $@ $(MYEXTLIB) ... )

Hi, unfortunately neither prepending LDDLFLAGS="-R$ORIGIN/../lib" to "perl Makefile.PL" nor editing the Makefile.PL:

WriteMakefile1(
  ABSTRACT_FROM => 'Parser.pm',
  AUTHOR        => 'Clark Cooper (coopercc@netheaven.com)',
  LICENSE => 'perl',
  MIN_PERL_VERSION => '5.00405',
  META_MERGE => {
    resources => {
      repository => 'http://github.com/chorny/XML-Parser',
    },
  },
  #BUILD_REQUIRES => {
  #},

  NAME  => 'XML::Parser',
  DIR   => [qw(Expat)],
  dist      => {COMPRESS => 'gzip', SUFFIX => '.gz'},
  VERSION_FROM => 'Parser.pm',
  PREREQ_PM    => {
    LWP => 0, #for tests
  },
    $^O =~/win/i ? (
        dist => {
            TAR      => 'ptar',
            TARFLAGS => '-c -C -f',
        },
    ) : (),
  dynamic_lib => {
      OTHERLDFLAGS => "-Wl,-rpath,\$ORIGIN/../lib"
  },
  @extras
);
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did work. In fact when I make, see the LD_RUN_PATH variable (it's always the same):

Running Mkbootstrap for XML::Parser::Expat ()
chmod 644 Expat.bs
rm -f ../blib/arch/auto/XML/Parser/Expat/Expat.so
LD_RUN_PATH="/root/perl5/lib" cc  -shared -O2 -L/usr/local/lib -fstack
+-protector Expat.o  -o ../blib/arch/auto/XML/Parser/Expat/Expat.so   
+     \
           -L/root/perl5/lib -lexpat    \

chmod 755 ../blib/arch/auto/XML/Parser/Expat/Expat.so
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If you want it to take effect for XML::Parser::Expat, you have to put the declaration in ./Expat/Makefile.PL, not ./Makefile.PL.

For example, your ./Expat/Makefile.PL could read:

...
WriteMakefile(
    NAME    => 'XML::Parser::Expat',
    C         => ['Expat.c'],
    LIBS    => $libs,
    XSPROTOARG => '-noprototypes',
    VERSION_FROM => 'Expat.pm',
    LDDLFLAGS => $Config{lddlflags}." -Wl,-rpath,$ENV{ORIGIN}/../lib",
+    # <-- add this
    @extras
);
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Sample build session:

$ ORIGIN=/usr/local/foo/bar perl Makefile.PL 
Writing Makefile for XML::Parser::Expat
Writing Makefile for XML::Parser

$ make
...
rm -f ../blib/arch/auto/XML/Parser/Expat/Expat.so
LD_RUN_PATH="/lib" gcc   -shared -O2 -L/usr/local/lib -fstack-protecto
+r -Wl,-rpath,/usr/local/foo/bar/../lib Expat.o  -o ../blib/arch/auto/
+XML/Parser/Expat/Expat.so    \
           -lexpat      \
...

$ readelf -d ./blib/arch/auto/XML/Parser/Expat/Expat.so | grep Lib
 0x000000000000000f (RPATH)              Library rpath: [/usr/local/fo
+o/bar/../lib]
 0x000000000000001d (RUNPATH)            Library runpath: [/usr/local/
+foo/bar/../lib]
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Similarly with the dynamic_lib => { ... } variant:

WriteMakefile(
    NAME    => 'XML::Parser::Expat',
    C         => ['Expat.c'],
    LIBS    => $libs,
    XSPROTOARG => '-noprototypes',
    VERSION_FROM => 'Expat.pm',
    dynamic_lib => {
        OTHERLDFLAGS => "-Wl,-rpath,$ENV{ORIGIN}/../lib"
    },
    @extras
);
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$ ORIGIN=/usr/local/foo/bar perl Makefile.PL 
Writing Makefile for XML::Parser::Expat
Writing Makefile for XML::Parser

$ make
...
rm -f ../blib/arch/auto/XML/Parser/Expat/Expat.so
LD_RUN_PATH="/lib" gcc   -shared -O2 -L/usr/local/lib -fstack-protecto
+r Expat.o -Wl,-rpath,/usr/local/foo/bar/../lib -o ../blib/arch/auto/X
+ML/Parser/Expat/Expat.so     \
           -lexpat      \
...

$ readelf -d ./blib/arch/auto/XML/Parser/Expat/Expat.so | grep Lib
 0x000000000000000f (RPATH)              Library rpath: [/usr/local/fo
+o/bar/../lib]
 0x000000000000001d (RUNPATH)            Library runpath: [/usr/local/
+foo/bar/../lib]
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(Note the "-Wl,-rpath,/usr/local/foo/bar/../lib" part in the linking commands above, and its different position.)