To make your profile invisible to all LuvFree users and visitors, log in to your LuvFree account which will take you directly to your "My Panel" page. From there, click the "Suspend profile" button in the "Manage profile" section on the upper right corner of the page. While in Suspended status, you can browse the site anonymously and no one can see your profile and you will not be allowed to send or receive messages to/from any LuvFree users including ones on your Friends List. You can remove Suspended status at any time by clicking the "Activate profile" button in the same place.
Searching for love I believe now in the right place.