You're going to need to accumulate the lines so that you can print the summary before the details. Something like this (untested):

# Your count and letters declarations here
my $accum;
my $banner;
while (<>) {
    if (/^L/i) {
        if ($banner) {
            print $banner, 'tstat propmean;elms=', @letters[0..$count-
+1], "\n", $accum;
        }
        $banner = $_;
        $accum = '';
        $count = 0;
    }
    elsif (/^N01/i) {
        s/\n/;ID=$letters[$count]\n/;
        ++$count;
        $accum .= $_;
    }
    else { $accum .= $_ }
}
print $banner, 'tstat propmean;elms=', @letters[0..$count-1], "\n", $a
+ccum;
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