Hi, Here is the settings for attribute, I'm pointing to same Entity Form where I have this lookup. I also created new form that allow create new record in this lookup Entity table and set that form here but still it doesn't display New button.

For drop down lookup fields value issue I have to perform below steps:
First add Entity Permissions
- Give Entity Name - Select Lookup field to your form
- Save it and Re-edit as what you created, as you do not see Add Existing Web Roles
- Select all Privileges
- Now Add Existing Web Roles - Anonymous Users
- Save it
Go to Entity Form
- Entity Form Metadata
- Add Attribute
- Select Lookup field that you are using in your form
- In my case I picked Control Style Render Lookup as Dropdown
- Save it
Now I can see the values in the dropdown