Each Friendship Lamp can only be connected to one GroupID at a time.
When one lamp is touched all the Friendship Lamps on that Group will light up. In groups greater than two you are not able to send messages 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 the lamp's settings and change the GroupID as you switch between groups.
Please take note that you can only connect your lamp to one group at a time.