File_exists doesn't seem to work correctly

I have a php script that I want to execute only if another instance of the script is not already running. I have this code:

$lockfile = __DIR__.'/lock.file';

if(file_exists($lockfile) == false)
{
    echo 'no lockfile. Job will execute.';
    $handle = fopen($lockfile, 'x') or die('Cannot open file:  '.$lockfile);
    $data = 'This is the lockfile';
    fwrite($handle, $data);
    fclose($lockfile);

    createLinks();

    unlink($lockfile);
}
else
{
    echo 'Lockfile present, job will not execute. Please try again later';
}

But it does not correctly check if the file exists. If I call the script with my browser, the lock.file will be created correctly (I see it with ftp) and then delete it. However, I can still run the script several times at the same time. If I create a lock.file with ftp, it does not execute the script. I searched for hours now, what could it be? Maybe I'm stupid, but I think this should work, right?

Edit: Jep, the herd did it. Thank you so much! Final code:

$lockfile = __DIR__.'/lock.file';
$handle = fopen($lockfile, "x");

if(flock($handle, LOCK_EX))
{
    echo 'no lockfile. Job will execute.';

    $data = 'This is the lockfile';
    fwrite($handle, $data);

    createLinks();

    fclose($lockfile);  
    unlink($lockfile);
}
else
{
    echo 'Lockfile present, job will not execute. Please try again later';
}