Travel plan for Interlaken from Lausanne

It's definitively possible. I would use the train to do that. It's definitively also possible by car. From Lausanne to Interlaken you need around 1:45 by car and from Interlaken to Zurich around 1:30.

However, more convenient and probably cheaper is the train. Checkout fahrplan.sbb.ch to get the schedule for this connection.

Assuming you want to visit Interlaken on a workday, the first train arrives in Interlaken at 7:57:

The last train to Zurich leaves in Interlaken at 23:00

Therefore, you have around 15 hours in Interlaken.

It is possible, but I would consider to visit Lausanne on a day and then Interlaken on another day. Like this you could visit Vevey or Montreux or Chateaux Chillon when you are in Lausanne.

And another time go to Interlaken and visit a mountain of your choice that day.

When visiting Lausanne and Interlaken in one day, you could take the Golden Pass train which starts at Montreux (I think), passing Aigle, Gstaad, Zweisimmen and ending in Spiez (I think) which is close to Interlaken.

In my opinion, the town of Interlaken is nothing special and not worth a visit when you are not going deeper into the mountains.