The purpose of two-factor authentication is to prevent logins to your account by someone who knows your username and password. If you lose access to your two-factor authentication there are two ways for you to restore access to your account.
1) If you used the mobile app based two-factor authentication you can recover by using your backup code that you wrote down when enabling two-factor authentication on your account. Please see this guide on how to re-activate using your backup codes: https://localbitcoins.com/faq#cp-2fa-reactivate
2) If you do not have the backup code, you will need to submit a two-factor authentication removal from the login page. We can not manually remove the 2fa from your account. First, enter your username and password. When the site asks you for your 2FA codes press the "Problems with two-factor login?" link and then the "Send two-factor removal request" button to request a removal of your two-factor authentication.
If you set up paper based two-factor authentication and you don't have access to the codes (lost them, wrote them down wrong etc), I'm sorry, but there is no way to recover the codes - you will need to submit the two-factor removal request.