You only need to dump her if she actually is lying to you. Even though she already lied to you about her stripping job, it is understandable why she didnt tell you, assuming her story is true. She didnt want to scare you away. Now for her story, it is very pluasable that she is doing the stripping job to pay for school, this is not uncommon.
Now heres the deal, you want to be unbiased about the situation, dont assume shes a lying *****, but also dont assume she's innocent. What you want to do is investigate. Since you say she is long term material, the investigation may turn out worthwhile. You may find out she is telling the truth and can be trusted. also keep in mind, just becuase she told you a little lie already doesnt mean shell tell big lies too (like some idiot has already posted, you know who you are). If this were true, then everyone is a big liar, becuase everyone has told little lies, and then youd be required to dump everygirl unconditionally.
Now heres one way you can start: One thing she told you is that she does not do lap dances. If you find out she really is doing lap dances, then everyone is probably right, this is the tip of the iceberg for the rest of her lying.
HERES HOW YOU CAN FIND OUT IF SHE IS DOING LAP DANCES:
Get one of your friends that your GF does not know, give him 20$ or the price of a lap dance, and send him into the strip club on a mission to see if she will give him a lap dance. If she really is giving people lap dances behind your back, shell just assume your friend who she doesnt know is just another paying customer, and she will gladdly give him a lap dance. Very easy. If shes honest, she should refuse your friend. THis is one way to test out if she lied about that. If she refuses the lap dance, then thats a point for her being innocent, but you still cant be sure. But if she does give a lap dance, then she has already crossed the line, and its grounds for you to dump her ass. But again, if she refuses, she could still have some other stripper job irrelevant secrets (maybe shes seeing another guy) who knows, but you need to investigate.
Another thing you need to do is ACT LIKE YOU BELEIVE HER TOTALLY, deception is a great tool to catch her. If shes a lying little *****, she'll be trying to cover up any evidence of her lies at this point, she is afraid your onto her true side(assuming shes lying to you about alot of things). And you dont want her to be covering her tracks, this will make it difficult for you to figure out if she's lying to you or not. But if you act like you totally beleive her, shell get a false sense of security, and take the lazy route, and not go out of her way to do things to cover her tracks on her lies since she thinks you trust her again. And this is what you want, if she's lying, you want her to not cover her tracks, you want her to leave lots of evidence for you.
I dont see it as a problem if shes just taking her clothes off. The problem here is that she may be doing more: lap dances, or may even be ****ing around with other men behind your back. THese are the 2 things you want to investigate. Be smart, and come up with clever ways you can find out if she is cheating on you. As long as you play dumb, shell leave her guard down, and this will make it easy for you.
I dont know enough about your schedule or hers or about your situation to suggest any good ways to catch her cheating on you, but if I knew if your work schedule is fixed or if it is irregular, or if hers is fixed or irregular, if shes always hanging out with her girlfriends when your working, if she supposedly goes straight home after work, etc. I could give your more tips and tactics. But for now, your on your own, good luck and happy investigating.