Need one more place

How are you traveling between these locations? By train? The reason I ask is that will eat up a full day Paris to Lauterbrunnen (nice trip). As it is 24 hours by train from Lucerne to Oslo (according to Rome2Rio.com), stop certainly seems in order. Copenhagen is on a direct route and you can fly out of Zurich.

Paris to Lauterbrunnen will be through train.
Lucerne(via Zurich) to Oslo will be through flight.

Are you flying to Oslo? From where? Between which 2 places do you want to "insert" the "one more" place? It depends mostly on flight and train schedules.

While it's tempting to just pick some "cool" places to visit, logistics are the key for planning a successful itinerary. And you need to take travel time into account. You need about 1/2 day for travel every time you move. Add at least 2 hours (3 or more in some places) to your train time for packing, door-to-door journey and checking in/out. Do you have 20 full days in Europe? Even if you arrive in the morning, by the time you get through the airport, into the city and check in to your hotel, you've used up several hours. Then you have to get your day packs ready and you are jetlagged and probably sleep-deprived, so on Day 1 you usually don't see or do much. Most flights to the U.S. leave in the morning, so your last day probably doesn't count either. Unless you have an evening flight out, you won't have much time to do anything that day, since you have to pack and arrive at the airport about 3 hours before flight time.

The plan include the travelling time between places and we are ok with it. The hotel checkout checkin time anf jetlag are accounted for. Moreover this is not yet hardbound plan so we can extend vacation if needed. Zurich to Oslo flight plan is also can be changed if some other city has to be fit in.

Guys any suggestions would be highly appreciated

Well I will cast my vote for Amsterdam then.
Amsterdam.. because its different then the other places you are visiting.
Contrasts are good..
It is flat ( so not like Lauterbrunnen. where you will love the mountain scenery) ..
It has canals and little cute bridges..
The people are pretty friendly..
Its not sophisticated and chic like Paris..but it IS vibrant and quaint.
Just a whole different vibe.. perhaps stop in Brugges for a day on the way between Amsterdam and Paris.. I find it too cute for me.. but most people love Brugges too.

I would look at what cities have convenient (direct) flights home, but I despise layovers.

If you picked Copenhagen, you could take an overnight ferry from Oslo.

Thanks all for suggestions. I might go with Amsterdam.