I don't think this is correct in general. Here's an example that demonstrates locking a file that has been opened for reading:

#!/usr/local/bin/perl -w

use strict;

use Fcntl qw/:flock/;

my $file = 'flock.test';

-e $file or open(FILE, ">$file") or die "Can't create $file: $!";

if (fork) {
    open(FILE, "<$file") or die "Can't open $file for reading in paren
+t: $!";
    flock(FILE, LOCK_EX) or die "Can't flock $file in parent: $!";
    wait;
} else {
    sleep 1;
    open(FILE, "<$file") or die "Can't open $file for reading in child
+: $!";
    flock(FILE, LOCK_EX|LOCK_NB) or die "Can't flock $file in child: $
+!";
}
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And here's the output it produces when run on my system: Can't flock flock.test in child: Resource temporarily unavailable at flock.pl line 18. However, this behavior is probably system dependent, so physi and I are likely both right.