I want to allow users to create records of a custom object from Site's public home page. I have created the page and can view the form correctly. I have used the standard controller for MyObject on the page. The form has two lookup fields which are two other custom objects (MyLookup1 and MyLookup2). When I click on the lookup icon, the authentication required page shows up instead of showing list of looked up object.

On site public access settings, I have given Read/Create access for MyObject and Read/View All permission for the objects MyLookup1and MyLookup2. All of these are custom objects created by me. How can I make sure that lookup popup will not ask for authentication?