So I've been talking to this girl recently. I got her number after class one day and we messaged for a week or so while I was in Amsterdam. Last Thursday I asked her to go out to lunch sometime, indicating my interest in her. I suggested we take a break from summer work and go out and she told me she needed to get some work done but she would next week. It's next week. Should I ask her again later this week or wait for her to bring it up?

You should ask her again. Nothing wrong with today.
When you ask someone out, don't say 'sometime.' Pick a day and time and occasion. She will either say OK, or 'good but let's pick a different day,' or she will say something vague. Given that you were vague, she was understandably vague. Once you get specific, you will have a better idea of her feelings.

Agreed. She needing to get some work done was probably an honest response.

Go for it, dude ��

Of course you ask her out again, but as was said be specific.