On Swiss trains, there is usually free seating, this is why your ticket does not have any seat assignments. Swiss trains are a form of mass transit, similar to suburban trains in other countries. As a result, you are welcome to take any vacant seat in your respective travel class. If you want to sit next to someone you don’t know, it’s courteous to ask if the seat is available before sitting down.
You will see once you are here how easy it is to use the Swiss public transport.
Should you reserve a seat? Except for certain panoramic trains (PE), seat reservations on Swiss trains are completely optional and not very common. Swiss people usually make seat reservations when they would like to eat in the dining car, when they travel as a group of 10 or more, or when many travellers are expected. If you still want to reserve your seat, kindly note that this is possible for IC, ICE, EC, IR, RJX, and TGV connections only: Seat reservations in trains and dining cars | SBB
→ Should a seat be reserved, it is indicated above the seat by either a yellow strip or a digital display.
→ Should you travel as a party of ten or more, a group reservation is recommended: Group tickets | SBB
A seat reservation is mandatory for Glacier Express, Gotthard Panorama Express, Bernina Express (for panorama coaches only), GoldenPass Express (not for regular trains and GoldenPass Panoramic).
_To answer your question: no seat reservation required for Interlaken to Lucerne; it would be optional and can be done here: Secure a seat | zentralbahn.ch. Simply take a seat on the right-hand side in travel direction (more scenic). And, for Lucerne to Zurich, you cannot make a seat reservation as the train is of category IR, for which seat reservations are not possible.
When do you intend to travel? See: PE Lucerne-Interlaken Express: line interruption from 2 October to 26 November 2023 - construction