Lucerne is too far away. It's doable, but the trip is very long so the weather may have turned bad by the time you reach Jungfraujoch after more than 4 hours of traveling. Interlaken and Lauterbrunnen are both a perfect base for this trip.
All you need to know about traveling by train, bus or car in Switzerland.
Hand picked Swiss hotels and other accommodations are right here.
Swiss Travel Pass promotion: 30% discountAvailable until 31 October 2022. Book 6 months ahead.https://shop.switzerlandtravelcentre.com/swisstravelpass