An approved LP is only as public as you make it! If you use a long, unguessable URL (like a random alphanumeric string) no one is going to just happen upon your page.
Once you start linking to and indexing your page, that's another matter -- you're inviting people to discover the page.
You can also generate an expiring Draft Preview URL:
Note, if you're extra paranoid: the preview is still technically public until it expires. It's merely unlisted with a hard-to-guess URL, not password protected. So, in the unfortunate event that someone pastes that link somewhere public, anyone who has the link can see it. Of course one doesn't expect such a worst-case scenario, but I want to be clear that this isn't a private URL per se.
Aside from making an un-guessable url, you can use dynamic content to better protect the landing page.
Create a segment for the specific email address/es you wish to allow access
Find a section you can add html and make it dynamic using the segment you created
Choose the default segment and add this script:
<script> window.location = "http://google.com" // or your homepage you wish to redirect users to </script>
Make sure the above is deleted in the "allowed" segment