Sorry for any confusion! Lumosity is a subscription site, like Netflix or your cell phone plan. All Lumosity subscriptions are set up with with automatic renewal, which can be cancelled at any time. You can find this information on our Terms of Service, our purchase page, under "your account" after logging in and in the purchase confirmation we emailed you.
Did you try to cancel renewal via your account pages or by contacting us via our help desk? If you did you should not have been charged for renewal. Contact us via the help desk now and we can look into what may have happened. Here's a direct link: https://help.lumosity.com/home