Take a look at this one of theirs:
Any mailing list over 900 emails is only allowed to be sent to during off-peak times to prevent high server loads. Off peak times qualify as all day Saturday and Sunday, and 1am - 8 am eastern time M-F.
So unless you are mailing during those times you are breaking their policy.
Besides that, it looks like if you throttle the mailing you should be somewhat ok.
You also say "Lists", which to me means more than one... If your total lists exceed 5,000, it appears you violate their rule.
I'd personally suggest finding another host.