When it comes to mailing lists, there's a standard practice where after someone signs up to your mailing list, you send them to a thank you page. This is where businesses might offer the subscriber a special deal on the business's products or services. (FYI: I am not using this type of page, but I really should.)

You can use this type of page to connect with the new subscriber and get them interested in your next book. You might also add a link to the lead magnet you promised, but I think that should instead be delivered by email.