Install OpenLiteSpeed from App Store
Uninstall Apache from App Store
Now restart the server
Remember, unlike Apache, OpenLiteSpeed doesn't update .htaccess automatically. That's why you need to restart the OpenLiteSpeed server whenever changes are made in the .htaccess file.
I recommended installing OpenLiteSpeed on the new server with a fresh aaPanel ➔ OpenLiteSpeed setup. It prevents compatibility issues with existing apps. Once the new server/aaPanel setup is completed, move data old to new server & change IP/name server as per the new location. This can be done with zero downtime if your DNS is hosted on Cloudflare (or an equivalent grade DNS service provider). Make sure TTL for related DNS records should be set to automatic for seamless transition of traffic to the new server.
Hope this information will be helpful in your Apache ➔ OpenLiteSpeed migration.