OK, I'm happy to report that with the help of my support ticket I am now connecting to the database. I thought I'd report the solution here, while it isn't difficult it certainly isn't intuitive so maybe I can help save some else's headache...
The issue I was having was all related to my database username.
When you create your database user in LPCP, type in the name and DO NOT CHANGE the IP address under hostname. Even though you are using lpsql01.lunariffic.com, that is NOT where you enter that information.
After you create your user, the name will show on your MySQLmanager as LoginName_DBusername@IPaddressProvided. That is fine.
When you enter your info into the WP-Config.php file, your username becomes LoginName_DBusername. Do not add on the @ or the IP address.
And your host name (formerly localhost) becomes lpsql02.lunariffic.com (or whatever server name you are given on your Critical Account Info data sheet when signing on).
And there you have it.