I wish I had a computer that executed 4380585.25 greps per second...

Your test is useless. The @data, $string1 and $string2 used by the test are always undef. I fixed it up below. Note the use of sub { ... } instead of q{ ... }. Subs capture over my variables, while the string is evaled in a different scope where the my varibles don't exist.

#!/usr/bin/perl

use strict;
use warnings;

use Benchmark qw( cmpthese );

my $string1 = qr/tr/;
my $string2 = qr/e/;

my @data = do {
   open(my $fh, '<', $0) or die;
   <$fh>
};

cmpthese (-3, {
   grep_and => sub {
      my @r = grep /$string1/ && /$string2/, @data;
      return @r;
   },

   double_grep => sub {
      my @r = grep /$string1/, grep /$string2/, @data;
      return @r;
   },

   lookahead => sub {
      my @r = grep /^(?=.*$string1)(?=.*$string2)/, @data;
      return @r;
   }
});
[download]

               Rate   lookahead double_grep    grep_and
lookahead    8114/s          --        -52%        -62%
double_grep 16986/s        109%          --        -21%
grep_and    21483/s        165%         26%          --
[download]

The contents of @data are probably not all that good, so the figures aren't perfect, but they give a pretty good idea.