Assuming your hotel is in the main part of Lucerne, you can easily do a walk around yourself. The main city sites are close together and easy to walk to - the Lion, Glacier Garden, Jesuit church, covered bridge and just the general architecture/old buildings to see. Nice little pedestrian area.
Best thing for jet lag is to get out in the sunshine for a walk around. If you arrive mid day odds are you won't be able to check into your room and would need to have the hotel store your luggage and find some way to kill time.
Rick Steves Switzerland guide book has a suggested walking tour. His Switzerlands Great Cities video includes Lucerne. He also mentions a little tourist train www.citytrain.com that does a 40 minute circuit. It's not a real train, just one of those cute mini trains that travel on surface streets.
For inexpensive eats, the train station has several dine in and take away options. Also in town the Manor department store is supposed to have an excellent restaurant (closed on Sundays).I
Best of luck. We're hoping to be there in Sep.