If you are sharing these file handles between threads, then you should be synchronising access to them anyway. Ie. declare a shared variable for use as a mutex, take a lock() on them before printing to them and release it afterward.

Something like this where the logging file is declared before the threads are started?

#!/usr/bin/perl 

use threads;
use threads::shared;

my $loglock :shared ; 

open(LOG, ">/usr/local/lease.log");

sub ilog{
 my $text = shift; 
 lock $loglock; 
 print LOG $text;  
}


## Start defining threads from here on
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From your post, this is what I gathered. This should work when multiple threads write to the log file and when one has a lock on the variable, the others cannot write until the lock goes out of scope.