Log into your LeagueRepublic account and click on My Account.
In My Account, on the top corner, right handside of the page, click on the link "Delete Account",
and press "Delete". If you are logging in with your username/password you will need to enter your 'Current password' before clicking on 'Delete'.
Note: Deleting your account will:
Delete your username and password from LR systems
Unlink your facebook login
Delete your email address
Deleting your account will not:
Delete any sites that you have set up (read Deleting a site)
Delete your first name and last name from any leagues you have participated in (you will need to contact the league to have your data deleted)