Well, yes! But you will need more than one lamp.
You, the user, can be a member of as many groups as you want. However each lamp can only be one group at a time. You can always add another lamp to your account and have it be in a different group.
In the example, you'll notice that Katie has one lamp that she might use to tell her roommate that dinner is ready while she has another lamp in a group with her best friend, for when she misses him.