Hi Lewis,
I am not 100% sure, but I have never come across a way to password protect a site using the GDI site builder. Of course, I have never tried but my gut is saying no.
However, here is something you could do.
Create a WordPress blog as a subdomain to your site. So you could have
www.members.lewiswhite.ws or something similar.
Then, do a search for WP plugins that will password protect your WordPress site. There are many out there, but I cannot suggest any as I have not personally used any. A quick search revealed a few that received a 5 star rating.
Then, on your site builder site create a link to "Members" or whatever, that points to your subdomain. When someone clicks that, they will need a password to continue further.
Let us know how it works for you or if you find another way.
Vincent Parker