Jill's Burgers was very close to our hotel (Hotel des Alpes) and we wanted to try a sandwich for dinner. We had the pork and both types of chicken sandwiches and they were very good. The sandwiches are large, so you may want to think about splitting them. The burgers looked good and are average size, so you may not need to share that one. The fries were good too. As with most restaurants in Lucerne, the sandwiches were pricey, about 20e each.
The restaurant is right on the river/lake and there is seating outside and inside. The beer was great too.
I would recommend Jill's Burgers.