Fun with bit strings :)

Here's compress and decompress subs with supporting hashes.
Using your test generator, I get about 55% compression most of the time. This is better than gzip or bzip2 on the one test case I tried. gzip was below 30% and bzip2 was below 45%.

There are pathological cases however. If you replace your rand(10) with 9 you will get a 675% expansion instead of compression.

The compressor maps 4 lines of your test input to 27 bytes and the decompressor does the opposite, so I suggest you compress in multiples of four lines, and decompress in multiples of 27 bytes if you have to split up very large files.
decompress(compress($string)) does reproduce the input string exactly, however, no matter how many lines are in it (at least in my testing :)

#!/usr/bin/perl

# https://perlmonks.org/?node_id=1233613

use strict;
use warnings;

my @legal = grep !/11/ && tr/1// <= 3, glob '{0,1}' x 8;
my %code;
@code{@legal} = map { unpack 'b6', chr } 0 .. $#legal;
my %decode = reverse %code;
$_ = [ split ' ', '23456789' & tr/01/ ?/r ] for values %decode;

sub compress
  {
  my $coded = '';
  for ( shift =~ /(.*)\n/g )
    {
    my @lookup = (0) x 123;
    @lookup[ unpack 'C*', $_ ] = (1) x length;
    for( my $group = 35; $group < 123; $group += 10 )
      {
      $coded .= $code{ join '', @lookup[$group .. $group + 7] };
      }
    }
  return pack 'b*', $coded;
  }

sub decompress
  {
  my $decoded = '';
  for my $line ( unpack('b*', shift) =~ /.{54}/g )
    {
    my $decade = 33;
    for my $group ( @decode{ unpack '(a6)*', $line } )
      {
      $decoded .= pack 'C*', map $decade + $_, @$group;
      $decade += 10;
      }
    $decoded .= "\n";
    }
  return $decoded;
  }

my $input = '';
for (1 .. 100)
  {
  for (my $x=0; $x<90; $x+=10)
    {
    my @c;
    push(@c, int (rand(10)+$x));
    push(@c, int (rand(10)+$x));
    push(@c, int (rand(10)+$x));
    push(@c, int (rand(10)+$x));
    @c = sort{$a<=>$b}@c;
    for (my $i = 1; $i < @c; $i++)
      {
      $input .= chr(33+$c[$i]) if $c[$i] != $c[$i-1] && $c[$i] != $c[$
+i-1]+1;
      }
    }
  $input .= "\n";
  }

#use Data::Dump 'dd'; dd $_ for $input =~ /.*\n/g;
print "\n     input length ", length $input, "\n";

my $compressed = compress($input);
my $compressedlength = length $compressed;
print "compressed length $compressedlength\n";
my $restored = decompress($compressed);
if( $input eq $restored )
  {
  printf "\nMatched, compression ratio = %.1f%%\n",
    100 * (1 - length($compressed) / length($restored));
  }
else
  {
  print "----------------------------------------failed\n";
  use Data::Dump 'dd'; dd $_ for $restored =~ /.*\n/g;
  }
[download]

Output of typical run (100 random lines) :

     input length 1507
compressed length 675

Matched, compression ratio = 55.2%
[download]

Thanks for the fun chance to play with long bit strings.