It is good to delete a cookie manually from your site. All you do is set the same cookie but with no value and with an expiry date in the past. This forces the browser to delete the cookie from the users system.
Delete lastVisit cookie from the users system:
setcookie ("lastVisit", "", time()-60000);
As shown, the value is empty and the expiry date is the current time() minus 60000 seconds, Any negative number will work but due to variations in computer times, it is not recommended to use -1 but instead something higher like a day or two.