Your girlfriend is an exotic dancer, yes. If people think any less of you for that, then they’re morons. However, morons can still hurt your profits, so you need to be careful. Don’t worry about the leverage thing. That usually isn’t a problem.
First, examine whether or not you really DO have an image that needs to be upheld and analyze how this may impact your business. You need to determine if “the juice is worth the squeeze”, meaning if she is worth whatever impact may occur.
Next, talk with her and determine why she felt the need to lie to you. Also ask if she’d feel comfortable laying low with her profession around your clients or coworkers if the situation ever arose. I am not saying to lie, but rather to be a little general with what she does for a living.
Finally, don’t even think about passing any sort of personal judgment for any decisions she’s made in her life. Yes, she lied to you because she may also feel remorse for who you are and what she does, but it doesn’t mean it’s a bad profession. She may be the “good one” who “does bad for a living”. If her profession is truly what is bothering you and not the fact that your business may or may not be tarnished, you need to take a look at yourself and figure out why you think you feel you’re superior.
It’s a tough decision. I hope you find whatever answer you’re looking for.