She presses her lips together at that question. Happy that Shadow can't see her face. It's not hard, but it's also not easy. Once she would have probably brought Oliver to the Arrowcave and everyone would have had a good laugh at the fact that he and Oliver shared a name. Oliver would have said 'This isn't funny Felicity.' in that grouchy gruff voice and she would have laughed. Now, she wasn't even sure he knew she existed let alone that they were anything even close to friends (let alone loved each other). In the end, there were days that it was hard, but she wasn't about to tell Shadow that.
"Oliver the cat is a lot cuter." She decides to say. Not entirely a no and not entirely a yes. Still, it wasn't lying to Shadow either. "Also, we need to change this not remembering what mint chip tastes like nonsense." She opens the door and lets the boy and lion inside.