If you are going on Holiday on Island Krk and wish to travel with bus from Lucerne you can do so. First part of the trip is bus from Lucerne to Rijeka, departure times and ticket prices for that route you can see below, once you arrive in Rijeka, you can continue with local bus to Island Krk, on Krk you can travel to Town Krk, Malinska, Punat, Baska and other cities on the island, timetable for buses between Rijeka and Krk town you can see here.
The total travel time from Lucerne to Krk is about 12 hours, if you plan also to travel back to Lucerne you should buy return ticket for both buses.