There is a scenario for anonymous users. Anybody on internet can fill form for a list.
There is validation for email id column to check duplicate entries. for that I have used calculated field which has lookup function.
If(isNullOrEmpty(lookup("List Name","Email",lblEmail,"Email")),"","Already registered ")
This is not working for anonymous users although I have given "Add items" permission.
Error says "A request for SharePoint data failed. Error details: Access denied.
You do not have permission to perform this action or access this resource."