Your Neighbor is not on a LAN with you. As such, you will not use the LAN connect option. VST Connect Pro 3 login will generate a numerical code, two sets of Numbers separated by a single space. Your Neighbor is to enter this code into their VST Performer application.
The number your login generate is a connection address generated by Steinbergs server. When your neighbor enters the code/address Steinbergs server connects the two or you. And As I understand it, once you are connected Steinbergs Server drops out of the connection, having assisted in your peer to peer connection.
If you are connecting via LAN, VST Connect Pro 3 login will initially hit Steinbergs server and generate the code, but as soon as you connect with VST Performer on the LAN the code is dropped and replaced with the LAN connection address.
As I understand it, Steinberg can see their server activity regarding connection code request. Probably also status of connections regarding internet and LAN connection counts over given time periods. Lets them know how much their VST Connect Software is being used. But Probably not how successfully the Software is being used.
Those in the know, feel free to correct me.