From Stuttgart Hbf train to Zürich HB then train to Luzern. 4 h 6 min 102€. From Stuttgart drive to Lucerne. 2 h 48 min 36€. From Stuttgart Hbf (tief) train to Stuttgart airport, fly to Zurich airport, then train to Lucerne. 3 h 58 min 121€.
German Railways (DB) operates a train from Stuttgart to Lucerne every 3 hours. Tickets cost $55 - $90 and the journey takes 3 h 2 min. Swiss Railways (SBB/CFF/FFS) also services this route every 30 minutes.