Wow. This suggested reading (even though it isn't exactly what I am doing) fixed it!

Sorry to say, Mitch, but now that I know this little trick, I am pulling my DNS hosting from Lunar Pages (you aren't very good at uptime anyway)!
This new found information will make my job administrating this crap so much easier!
Especially now that I can do it myself without having to go through support (you
really need to get that changed)!!!
Solution:- I added new.nonlp.com to my "Add-on domain list"
- At ns.nonlpDNS.com, I added an A record for new.nonlp.com to my LP server IP Address.

Voila! Presto Chango!!!
No, it's not at new.mylp.com, but that'll do, pig, that'll do!!! I am so excited at getting this little nugget working!
I can use my non-Lunarpages DNS to make DNS changes!!!! YAY! 
Mitch, I could hug you right now!

THANK YOU!
ps That is more smiley's than I've ever used on the Internet, ever, total.