If I understand the OP correctly, you can add a scope to instantiator I believe you can get the desired effect e.g

{
  my $both;
  sub inst {
    my $inner = shift;
    $both .= "xxx ";
    return sub {
      printf "both: %s\nmine: %s\n", $both, $inner;
    };
  }
}

for( 1 .. 3 ) {
 my $n = inst("[$_]");
 &$n;
}

__output__

both: xxx
mine: [1]
both: xxx xxx
mine: [2]
both: xxx xxx xxx
mine: [3]
[download]

So with the additional scope both inst and the newly generated sub will refer to the same lexical variable ($both).