Is it worth buying the Swiss pass if I am only traveling from Zurich to Luzerne and Interlake areas over a full 3 day period?
If costs is your main concern, then you need to compare all the costs that you plan to cover with the pass. Returning to Zurich or? Mountain lifts and trains (often more expensive than the legs you'll cover by regular trains)? Museums? Will travel be limited to 3 days or possibly 4 (affecting the choice of pass)?
See some of these laid out on our Swiss rail page as well as more detail around Interlaken and around Pilatus, for instance.
If that's too much to decide, then a Swiss Half Fare Card should at least save money over buying full-fare tickets.
So you're only staying in Interlaken?? You're not going to visit the alps? Interlaken isn't in the Swiss Alps. You will need to travel onward to Lauterbrunnen, Wengen, Murren, etc. Choose a hotel in one of those villages and do not waste time in Interlaken which is best used as a hub of rail connections.