You can physically do both. Lucerne is west of Zurich, Interlaken is further southwest under the Jungfrau. The day becomes a corridor of motorway and a few famous views through glass. Families with small children and anyone who came to shop in Zurich usually regret it by 16:00.
When we would still do it
- You have only this one spare day, you have already seen Zurich, and you accept that neither town gets a proper lunch.
- A private car, not a coach with a fixed photo stop. Flexibility is the only thing that makes the mileage human.
The better split
Day one: Lucerne and the lake, back to Zurich. Day two: Interlaken or a mountain if the weather is clear — fog on the Jungfrau is a long drive for a white wall. Tell us how many days you actually have; we will say no when the map is lying.