Recently I asked my ATF out to dinner making sure she realized it was on a social level and not a paid session.  She accepted pretty enthusiasticaly.  Since her agency would fire her instantly if they found out, I think she may be interested in being a little more then friends.  I don't plan to initiate any sex afterward because I can't afford another session so soon after the last and I think it would be unfair to expect a freebie.  
My question is what if she initiates sex and money is never mentioned.  Am I expected to still pay?  btw, I'm aware of the pitfalls of getting involved with a provider.

Beerguy – a  lovestruck teenager, a horny desperate man, or someone drinking way too much to think straight (beerguy moniker not withstanding might get carried away and ask questions or accept any awkwardness afterwards.

Everyone else would at least skate around the subject at dinner or at least once preliminaries were in progress (tricky though. Anything else will be setting one (or both of you) up for a fall and potential embarrassment/bitterness.

Of course lunch may simply be ‘lunch’ and even if she’s attracted to you – just because she’s an escort doesn’t mean she’s about to offer you desert.  

If you're single, have the financial means and the emotional stability to date your ATF; God bless you and go ahead. Just be warned beforehand that most of these situations end up in some form of disaster.
  From your post, I gather her agency will not be thrilled. Are you (and she)prepared for the financial consequences if she's fired? What if she comes to you for money or, perhaps, to lay a guilt trip on you?
  What will you do if she has misread your intentions? She figures you two are going for dinner (but no sex)as provider/client not potential boyfriend/girlfriend?
  There was an excellent post by June Cleavage several days ago on this very subject. It should be mandatory reading before you embark down this road. Good Luck.

I would gently ask her this in as tactful a manner as possible if it starts to go in that direction after dinner. Try something like this: "I don't want to be rude or for this to be awkward but just so there's no misunderstanding, am I a client right now or is this more personal?" Depending upon her answer you can then make your own decision. But don't go into the dinner with any expectation of a freebie -- this way you won't be setting yourself up for disappointment. And I wouldn't use clumsy euphemisms like "freebie" or "off the clock" -- it cheapens the moment (no pun intended). Good luck.

You are SO easy that you have sex on the first date?

You don't make the girl WORK to get your favors?  Show you that she values your mind and doesn't think of you as a piece of meat? Another notch on her belt?  Bragging rights to her friends down at her local bar?     Well, OK .. me too.

This is a situational deal and you just have to feel your way through it [pun alert].   If things are going well and SLOW, like kissing and fondling & stuff ... don't see that as an open door.   Maybe even make a joke that you're note a "first date" kinda boy.

On the other hand .. if she jumps your bones and simply over powers you ...  well, what can ya do?

I did not want to risk my personal life, I work in a law firm, too risky. As far as her, we had a falling out anyways, but will try to patch up.

Thanks to everyone who replied.  There was good advice in each. First about the moniker.  Don't drink very much really.  I used to brew beer for a hobby until I ended up with gallons and gallons of it in my basement.  I really should come up with a new name.  
I plan to approach dinner as I would with any woman on a first date.  Just have fun, enjoy the company and not expect anything more.  Good point Megapig.  Maybe I shouldn't be so easy!  Come to think of it, at the last session she took control of the situation and it seemed like I spent more time pleasing her than vice versa (not that I mind).  Maybe I'm just a booty call.  I will search for the post by June Cleavage.

Just my two cents, but I had an ATF once that at the end of each appointment I would tell her, " Gee, I should just take you out to dinner." Finally she asked me when I was ever going to get around to asking her out. We went out for a couple of months. It was not a client/provider relationship. It didn't work out there was no drama, we both just realized that we were not right for each other, and moved on. The sticking point was not her job, or anything to do with it. I played the first date like a first date. If it is a date then treat it like one and go in expecting exactly what you would on any first date.

How do I find it?  I tried a search on this forum for the last 60 days using June cleavage as author's name.  Nothing came up.