What to text when she wants to try axe throwing someday

The phrasing "I'd love to try" paired with "haven't had the chance yet" is an open door, not a request. She is telling you a preference and letting you decide what to do with it. The "at some point" and "lol" make it low stakes on purpose. If she wanted you to plan something, she usually says something closer to "want to try it sometime?" or names a day.

Read it as information about what she enjoys. It tells you she likes active, slightly silly things, probably with a bit of competition. That's useful whether or not you ever end up at a venue together. Treat it as a fact you now know about her, and let the next move come from how the conversation actually goes.

Before you respond, check whether you actually want to do this. If the idea appeals to you, say that in a sentence and mention one specific reason it sounds fun. If it doesn't, you can still ask what appeals to her, which gives her room to talk and keeps you curious rather than pushing your plan.

The quickest way to go wrong is to skip past her comment and redirect to something you want to talk about. Stay on the thing she brought up for at least one exchange. You can move to a plan after she has responded and shown she wants to keep going with the topic.

If she replies warmly and keeps the topic going, you can gently raise the idea of going once, something like suggesting you look up a place together. If she gives a short reply, shifts to a different subject, or doesn't pick up the thread, drop it for now and let it sit. Wait at least a few days before you bring it up again, and only if something in the conversation gives you a reason. Repeatedly returning to the same idea reads as needing her to agree to it.

If you do make a plan and she goes quiet, don't chase. Send one message that's easy to answer, and if that gets nothing, leave it alone. The thing she said can still be true later, and a light callback in a new conversation will do more than a second push.