Rogue kinda catches them but doesn't manage to kill them because she's not very bright, hunting-wise. She doesn't make the mental leap between hunting something and eating it. Food is bite-sized cooked morsels of food that come out of a can or from the Human's plates, but it doesn't come from the animals you catch. Those are Toys.

Lennon, however, is a mouser of extreme skill and fortitude. He'll bring down giant rats and gobble them up. He is a tiger.