The hostname you are redirecting from () already has the
www.
prefix.
You set the CNAME for www to addwww.redirect2.me, which means it will try to redirect to itself, which is not very useful.
If you want to redirect from www to root: set the www CNAME to removewww.redirect2.me.
If you want to redirect from www to another domain: set the www CNAME to lookup.redirect2.me and add a www TXT record with the value redirect2me=www.mynewdomain.com.