Hi Tracey,
Dean is absolutely right on this one. Once you implement a signup form to subscribe users directly into LMP, you will be able to send them an autoresponder thanking them for signing up. Of course, be sure to also include some sort of a marketing message along with that thank you note.
To add the autoresponder, go to:
List Setting >> Welcome & Confirmation >> Edit Message "Send welcome email on signup or when confirmed"
Good luck!