To kiss or not to kiss on 2nd date?

So we caught up (technically first dates are all about catching up and getting to know each other better), we had lunch and coffee. Then walked to the park and chatted for another 3 hrs! I'm quite sure she's keen. We spoke deep about our past relationships and what we want from the next partner as well as complimented each other.

The convo was full of serious topics with some laughs in between, she being aquarius and i Sagittarius meant we got along just fine and the chatting was flowing for the whole 3 hrs.

Now, i drove her home, i didn't go in for the peck in the lips, rather we pecked each other on the cheek. I didn't want her to think I'm only after sex or want to move things fast. After all, im 30yo and she's 33yo.

I messaged her the next morning saying i had a great time and we should do it again, she messages back Instantly saying she was in the midst of messaging me too saying the same thing and next time she'll pay coz i paid for the first time.
Anyway, we've been chatting since then and she's shown signs by text that she's defs keen!!
Now I'm excited and i really want to kiss her!!

To women... please advise if it's a good idea if i can kiss her on the lips on the second date or should i wait till the third?
To kiss or not to kiss on 2nd date?
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