You can lead a horse to water but you can't make them drink!!
As you probably know children's appetites can fluctuate a lot. I would just keep on doing what you are doing and not give her extra attention for not eating her meal. If she says that she is hungry before your scheduled afternoon snack do not feed her snack early....feel free to say...with lots of sympathy "I wish you had eaten more of your lunch" and then wait for snack time to roll around.
....she will figure it out. She won't starve. She is either not hungry or looking for extra attention for not eating. Some parents turn themselves into short order cooks trying to accommodate picky eaters....not me...you get what you get and you don't throw a fit. She is already getting a lunch packed by a loving parent full of nutritious food that the parent knows she will eat. Don't sweat it....you can lead a horse to water but you can't make them drink!