Each Luvlink Friendship Lamp can only be connected to one GroupID at a time, though you can add as many lamp as you'd like into a single group.
When one lamp is touched all the lamps on that group will light up. In groups greater than two, you will not be able to send greetings to individual lamps. Instead, all lamps on your group will light up when you touch your lamp.
If you do not want the other lamps on your GroupID to communicate, you will need to start a new group, with yourself having multiple lamps.
However, when the lamp is set up using the Luvlink app, you can easily go into your lamp's settings and change or toggle the GroupID as you switch between groups.
Please take note that you can only connect your lamp to one group at a time.