Looks like OnLive and Logitech are working together on a promotion where Logitech is bundling OnLive promo codes with OnLive compatible controllers they are selling. On the picture below you can see a 50% off any OnLive game promo code bundled with the Logitech Gamepad F310.
OnLive supports XInput compatible controllers. So, if you are using a Logitech gamepad, just make sure that it's set to XInput mode when using OnLive. Here is more info from OnLive on gamepad support and as you can see they also have Logitech controllers listed as supported.