Also, if the person does not respond positively (and I don't mean they respond negatively, but if they say no for whatever reason), don't ask again. They now know you want to and will let you know when they're free, and once they do, even if you're the one whose busy, you'll know you're not bothering them.
At least in Israel, lunch is regarded as inherently acceptable in a professional setting, since it's in the middle of the workday, even if you're eating out. Generally I'll only ask people to meet on their personal time if I feel like we know each other well enough and they like me back, otherwise it's an inconvenience -- asking for somebody's personal time is a big ask. With the opposite sex, I find it's really hard for a simple invite for dinner or beer to be misconstrued as an advance. It also helps that the vast majority of female engineers I know are in a relationship, so that makes my intent blatantly obvious.