I see that there is a way to customize the Welcome email, but it looks like the same Welcome email goes out for every list subscription.
Is there a way to generate a completely different welcome email based on which list is being subscribed to?
Unfortunately at this point there is only one welcome email, which will be delivered to anyone that joins the list using the "ACTION_BY_CONTACT" opt in source. You can find more information about this in Opting-in A Contact.
The only alternative that I can offer at this time would be to set certain subscribers up on an autoresponder list. This would allow them to recieve a series of emails set up at specific intervals. Unfortunately there is only one set of autoresponder series that can be sent out. For some more information regarding autoresponders, I would recommend viewing this FAQ.
I apologize for any inconvenience that this issue has caused. Please let us know if you have any other questions.