use strict;
use warnings;
while (<DATA>) {
 print unless ( /^Header1$/ .. /^END LIST$/ );
}

__DATA__
Header1
1 2 3 4 5 3
2
43 43
END LIST
Header2
2 42 24 2 32 2 32
2 2  4 2 3 
END LIST
Header1
2
43 43
END LIST
Header3
2 3 4 32 
3 4 3 43 
END LIST
Header1
1 2 3 4 5 3
2
43 43
END LIST

##</code><code>##

perl -ni.bak -e 'print unless ( /^Header1$/ .. /^END LIST$/)'  filename
##</code><code>##

my $text = do { local $/; <FILE> };
if ($text =~ /^Header1.*?END LIST/m) {
....
}
##</code><code>##

my $text = do { local $/; <FILE> };
$text =~ s/^Header1.*?END LIST\n?//msg