Let $G=\{cat,apple\}$ and $M=\{Meows,Fruit\}$
then
$C(G,M,I) = \{(\emptyset,\{Meows,Fruit\}), (\{Cat\},\{Meows\}),(\{Apple\},\{Fruit\}),(\{Cat,Apple\},\emptyset)\}$
And the lattice looks like this with the empty set on top and bottom. Is this allowed?
Update: I thought about it more last night, and I guess it depends on if you are showing the intent or extent on the lattice. If we we write the intents, the second empty will become {Cat,Apple} instead