In this case we recommend the following steps:
1. Change your primary domain from your Hostlantern User Area > My Accounts > Manage Account (for the account whose primary domain you wish to change) > Change Primary Domain.
2. Park your old domain name in cPanel, Parked domains.
This will allow your site to work by both your old and new primary domain name.
If you are not yet a customer, check out what our domain services include and how we can make your life easier. Managing your own domain is easy when you have the right host by your side.