Mail in 10.7.5 not syncing with iCloud (Oct 2014)

I have the 2-Step Verification set up. Recently Apple emailed everyone about creating third=party passwords for the 2-Step verification system. Well ever since that email sent, I cannot access my iCloud in my Mail 10.7.5. I've tried updating my password via System Prefrences > Mail, Contacts & Calendars and it ask for my iCloud password. So I enter it and ask me for my verification code and then ask for the password again. Then I get the Apple iCloud Terms and Conditions, which I do accept and click. Then here I'm stuck in a loop: it ask for my password and then ask for me to accept the Terms and Conditions! What the heck!

I tried clearing my Keychain passwords but I still get the same error/loop cycle. Should I enter through the actual Mail program (even though I read that I should go to my iCloud preferences based on this link: iCloud: Mail server settings for email clients)? Need help asap!

~L