Can I assign a 3rd party email list to each form?

Yes, you can but for integrations that are available in our form builder only.

We have the following email integrations:

MailChimp (https://www.jotform.com/help/163-How-to-Integrate-with-MailChimp)

Constant Contact (https://www.jotform.com/help/386-How-to-Integrate-Form-with-Constant-Contact)

Aweber (https://www.jotform.com/help/387-How-to-Integrate-JotForm-with-Aweber)

Campaign Monitor (https://www.jotform.com/help/388-How-to-Integrate-JotForm-with-Campaign-Monitor)

GetResponse (https://www.jotform.com/help/397-How-to-Integrate-Form-with-GetResponse)

Mad Mimi (https://www.jotform.com/help/396-How-to-Integrate-JotForm-with-Mad-Mimi)

iContact (https://www.jotform.com/help/398-How-to-Integrate-Form-with-iContact)

VerticalResponse (https://www.jotform.com/help/399-How-to-Integrate-JotForm-with-Vertical-Response).

I hope that helps. Please let us know if your email provider is not one of the above integrations. We can send that to our developers as a feature request.