Here is a list of Cafés that I have visited so far in Lucerne, each and every place has its own flavour and atmosphere, some are also restaurants while other even offer co-working spaces, include a shop or can be perfectly combined with a visit of a Museum or the Cinema next by (in alphabetical order):
Alpineum : https://www.facebook.com/alpineum/
Next to the Löwendenkmal. A small but cosy place. Can be crowded in peak times (lunch time, afternoon tea time, apero time) but
Bistro-Bar Bourbaki : http://www.kinoluzern.ch/bar-bistro/info.html
A drink or coffee can be perfectly combined with a movie at Bourbaki Cinema or the Museum in the same building (http://www.bourbakipanorama.ch)
Café de Ville – Schwanen : http://www.cafedeville.ch
Noble and traditional Café, lots of magazines, terrazza was in renovation when I went there, beautiful views (also soon again from the terrazza).
Café in the Museum of Arts : https://www.kunstmuseumluzern.ch/cafe/
This Café is located on the 4th floor of the famous KKL building next to Lucerne’s main Station. Can be perfectly combined with a visit to the Museum of Arts. Offers a nice ambiente and beautiful views to over the bay and lake.
Café Lokal : http://www.cafe-bar-lokal.ch/
A tiny place but apparently well known and frequented by locals, that’s probably somehow the hint for its Name. Next to Museum of history and nature. Reuss-river view.
Café Sowieso : http://www.cafesowieso.ch/home
Social Enterprise with arts Exhibition in the Café/Restaurant. Local seasonal cuisine.
Chez Cassis : www.chezcassis.ch
A colourful and cosy place. Combines coffee and a shop and they also organize concerts.
Heini : http://www.heini.ch/content/14-standorte
A number of traditional (“tea-room style”) Cafés invite for a coffee/tea with a nice Piece of cake or salty dish.
Mardi Gras : https://www.facebook.com/pages/Mardi-Gras
Friendly Service, nice and arty place. Cakes, magazines. Attracts a mix of People.
Mill’Feuille : http://www.millfeuille.ch/
Offers a beautiful view onto the Mühleplatz and river Reuss. It is also a Restaurant. Nice atmosphere.
Neubad Bistro : http://neubad.org/Bistro
It used to be a bath that has been transformed into a creative and collaborative space. It has a nice coffee/restaurant place, work spaces, Shops inside and different Events are organized.
World Café : https://www.kkl-luzern.ch/de/your-visit/dinieren-logieren/world-cafe
I like the atmosphere, most beautiful and irrestistible deserts. Offers also finger Food and international wok dishes.
viafranziska.com 
Wow you know the cafés in Lucerne better than us! greeting from Vietnam Dao & Markus
I’m grateful for the information provided… one more reason to plan my next visit 🙂
Definitely, dear Jasmine, we can make a cafe-marathon :))