Your Lightroom subscription is tied to your original iTunes ID. When our app launches, I think it checks to see if there are any subscription updates, and this causes the messages you've seen.
I don't know if Apple can refund you since you already committed to a year of service in advance, but since they control subscrioption transactions it couldn't hurt to reach out to their Support team and ask what they can do. If they could migrate your subscription to your new iTunes ID, that may help, but I've never heard that any such thing is possible. At the very least, perhaps they can force your subscription to end on your original account (if you cannot do that yourself) so that you can eventually resubscribe to Lightroom with your new iTunes ID. I wish I could offer more help, but Apple owns app store transactions. On our side, your Lightroom account with Adobe should remain subscribe for the remaining portion of your paid year of service. Soon after that lapses, you should then be able to resubscribe with your new iTunes ID.