Hi,
If you want to use Azure DNS to resolve queries for your public domain, you need to update the list of DNS servers for your domain at your domain registrar. You would change them to be the four Azure DNS servers that are shown in the Azure portal. Below are instructions for changing in Amazon route 53, which appears to be your registrar:
Updating name servers to use another registrar
https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/domain-register-other-dns-service.html
Once you make the above change at your domain registrar, there will be a delay for the change to propagate and then your nslookup will succeed.
Alternatively you could just create/modify DNS records on your domain registrar's servers and then you wouldn't need to use Azure DNS.
Please click Accept Answer and upvote if the above was helpful.
Thanks.
-TP