We will be traveling from Amsterdam to Lucern, by train. Stops along the way?

If you have time, I'd strongly recommend Bruges, Belgium, Bacharach, Germany, Strasbourg, France and the Lauterbrunnen Valley in Switzerland. We visited each by train in the past month and they were the highlights of our trip.

When are you traveling and how many days do you have between Amsterdam and Lucerne?

We can be flexile - but probably 4

I'd strongly recommend Bruges, Belgium...

I can't imagine Bruges being anywhere "on the way" between these two cities.

With four days you do not have to travel in a straight line. Paris for example is a perfectly viable stopover as well.

Cologne, Boppard, Strasbourg. 1 night in each and you'll be in Luzern by the end of day 4.