Confused on interpreting IOI and how I should react

Hello all, I am having a problem matching up ioi with a girl's actual actions or reactions.

To give some background I'm a college student and I've had several iterations with this girl, I'll call her Lisa, all within a group (mutual-friends) setting. When I first met Lisa, very early I noticed that she likes to touch/or play hit me when I tease her, make a joke, or say something--jokingly--that would solicit a comforting gesture; like her patting me on the back.

However, what confuses me is that on two occasions, she wouldn't let me walk her home. Since she lives on campus... she has insisted that it is fine and she does it all the time after studying late in the library.

Yet, even after such refusal, I still get strong IOI when I met her at our group events.

I am unsure what should be the next steps.... ask her out to coffee/lunch/dinner? Or wait for a stronger IOI, like an increase of texts from her, etc.