"He's not a tiger," Tigerlily scoffed faintly. Not that she would know - she wasn't entirely sure what a tiger was. "And he wouldn't eat me." Well, he might if he were particularly hungry - Tigerlily knew better than to actively befriend the creatures who lived in Neverland - but she did admire them, and have affection and respect for them. She liked to think that that respect was returned - though in all honesty, perhaps it was just that she kept her distance from them.
When Tinkerbell started to follow her, Tigerlily pretended to be highly annoyed and skeptical about the fact that her house was nearby. Her expression and attitude indicated as much. Though in reality, Tigerlily was pleased by this behaviour. She didn't see many adults in Neverland - with the exception of the Jolly Roger crew - and the idea that this woman lived here - had a house here - and Tigerlily hadn't known about it was strange to her. It meant her parents had done a better job "sheltering" her from Neverland than she'd realized. She was curious about the woman, and enjoyed the opportunity to get a better look at her.
"How do you live here and I've never heard of you?" she asked, forgetting for the moment that she was meant to be ignoring the woman, as they were suppsed to be travelling their separate ways. Also forgetting they hadn't actually introduced themselves, so for all Tigerlily knew she had heard of her. But those sorts of details seemed rather trivial to her now in the light of something new and interesting to learn about.