Maybe you could try asking the professor/TA or whatever a question so that you won't awkwardly just be sitting there while you wait for her. If you ask her to lunch she should get the message, without it being overbearing. If you just say something along the lines of "hey, so do you wanna grab lunch this weekend? I've been wanting to go to/try out _____ and it could be fun." Or however you would say it but to that general effect.