The calculated distance (air line) between Zürich (Kreis 3) and Luzern is approximately 23 miles respectively 37 kilometers.
By car or train, the actual journey to Luzern is certainly longer, as only the direct route (as the crow flies) between Zürich (Kreis 3) and Luzern has been calculated here.
Air line (approximately)
37 kilometers
20 nautical miles