use File::ReadBackwards;

$bw = File::ReadBackwards->new( 'log_file' ) or
                die "can't read 'log_file' $!" ;
until ( $bw->eof ) {
     last if ($bw->readline =~ m/$search_string/);
}
$prior_line_1 = $bw->readline;
$prior_line_2 = $bw->readline;