Flying to Zurich mid May- thought of making way to Lucerne for the three nights and doing side journey. We always wanted to go to Montreux. Now hearing Lugano is lovely.. Nice train journeys but just not sure what to do?
You do not have time for Lugano or Montreux. Just go direct from Zürich airport to Luzern (70 minutes by train) and soak up town+lake+mountains.
Use one day (the one with the best weather) to go up a local mountain (Pilatus, Rigi or Titlis).
Use another day for a boat trip on the lake.
What I would suggest is 2 nights in Luzern, and 1 in Basel.