If I've understood what you want to achieve (showing the output you expect would help), the following may do the trick:

use strict;
use warnings;

my %tags;
my $printing;

while (defined (my $line = <DATA>) || defined $tags{IT}) {
    if (defined $line) {
        my ($tag) = $line =~ /^{(\w+)}/;

        if (! $tag) {

            print $line if $printing;
            next;
        }

        $printing = $tag =~ /^(TAG|ID)$/;

        if ($tag ne 'IT') {
            ++$tags{$tag};
            next;
        }
    }

    print $tags{IT}
        if (! $tags{LINE} || ! $tags{ID}) && defined $tags{IT};

    %tags = (IT => $line);
}


__DATA__
{IT} 343
1
{DATE}
090104
{LINE}
LEGISLATORS  VISIT SENIOR APARTMENT COMPLEX
{TAG}
1lutherridge0104.ART
{ID}
234
{IT} 434
2
{DATE}
090104
{LINE}
LEGISLATORS  VISIT SENIOR APARTMENT COMPLEX
[download]

Prints:

1lutherridge0104.ART
234
{IT} 434
[download]

The key is to 'remember' what has been seen and perform the extra processing when the next section is detected. Note the tricky stuff that gets the last section handled correctly when the end of file is reached.