I don't know how to take that next step - how do I go from having lunch with this woman to going on a date with her?
The lunch
is the date, that doesn't necessarily have to be explicit.
Here's the thing: if you're both having fun, you'll see each other again. Of course it's always a good thing to cautiously check if she has the same intentions so you know you're both on the same page. If there's friends you have in common that are close to her while you trust them as well, you could maybe ask one of them if they can drop a hint/go "fishing" for information a little.
Ask her on a date.
Seriously.
Just do it.
And this. Be assertive. Dates don't plan themselves. However, it's generally wise to avoid the word "date" because it carries a lot of baggage. Just ask her out for something to eat, or something to drink, or whatever you want to do. If she isn't interested, she'll let you know and you can both move on.
