Just a little reminder: you forgot to explicitly unlock the file after the operation. I think this may be optional, but IMHO it always a good thing to do it explicitly, so your code should look like:

open(FH, ">>lock.txt") or die "can't open lock.txt: $!\n"; 
flock(FH, 2) or die "Can't flock lock.txt: $!\n"; 
now_access_the_common_resource(); 
flock(FH, LOCK_UN);
close(FH);
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Best regards,