Friendship Lamps can actually only be in one group at a time. When you attempt to add a lamp to a second group, it will remove itself from the first group. This will leave your name in the second group but say, "No Friendship Lamp", since you removed it.
For example, if you would like to have a group with your best friend and your sister, but not have them be in a group together, you'd need to have two Friendship Lamps at your location. You'd need to have one lamp for your sister's group, and another lamp for your friend.
Still having trouble? Please contact us and we will be happy to help!