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