You are right to be leery. Most of Lincoln Park is zoned, so you can't park overnight without a zone sticker. If you find an area that isn't, you also have to make sure there isn't street cleaning coming up.
You'd be cheaper to drive the van to ORD and park there for cheaper.
Long term parking at Ohare.
If must in Lincoln Park, have one of her friends in Lincoln Park with Zoned parking get your zoned parking stickers for the duration of the trip