Take This Lollipop Facebook application does not store any of your personal information. It is intended for entertainment purposes only and will not share your information at any time.
The "Share Box" at the end of the application is entirely user optional, and will only post the message you enter in, along with the description of the site takethislollipop.com which is shown in that box.
None of your Facebook information is transferred to an external server. It is only shown in your browser client at the time you view the application, and only available if you are currently logged in to Facebook with your account.