My first thought was to write a file to disk (a lock) and remove it on exit - so the next process will know to die... but what happens if it quits (or is killed) without removing the lock? Then nothing runs...

When a process dies, the OS removes any and all flock locks placed by it. Instead of checking for the existance of a lock file, check if there's a lock on it (after unconditionally creating the file).

Checking for existance is flawed anyway. For example,

Process 1                       Process 2
-----------------------------   -----------------------------
die if -e $lockfile;           
                                die if -e $lockfile;
                                open(my $fh, '>', $lockfile);
                                # I think I hold the lock.
open(my $fh, '>', $lockfile);  
# I think I hold the lock.     
                               .
                               .
                               .
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