Your ignored the fact that the search was case-insensitive.

my $host = lc(shift(@_));
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Your grep is wrong.

my @lines = grep { lc($_) eq $host } @ry;
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Why read the whole file everytime?

use List::Util qw( first );
my $line = first { lc($_) eq $host } @ry;
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Why use Tie::File if you're not going to take advantage of it?

use List::Util qw( first );
my $line = first { lc($_) eq $host } <$fh>;
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Why load up the entire file into memory if you look at it one line at a time?

sub get_comments {
   my $host = lc(shift(@_));
   my $file_name = "myfile.txt";

   open(my $fh, '<', $file_name)
      or die("Unable to open server info file \"$file_name\": $!\n");

   while (<$fh>) {
      return $1 if /^$host:\s*(.*)/;
   }

   return;
}
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Of course, that's still very expensive if get_comments is called repeatedly. If the list is really that long, some sort of index (or database) would be very useful. A sorted file with fixed length records would also be fine (allowing for a binary search).