Hi Tracey, and welcome to MySwissAlps!
>> Are restaurants or grocery stores open on Chrismas Eve in Lucerne, Switzerland?
I can’t give you a comprehensive answer to this question, but will make a start that hopefully others can add to.
As you are starting off from Zürich, your best bet for groceries on Christmas Eve would probably be Zürich Hauptbahnhof (main station), where the shops are open until at least 18.00. There is a large shopping centre in the lower level of the station.
The Migros grocery store at Luzern Bahnhof (railway station) is also open until 18:00 if you can get there before that time. This store is also in the lower level of the station.
Any restaurants that are open for dinner on Christmas Eve are most likely only offering “festive” dinners rather than “normal” dinners.
There is an earlier thread here that might help:
http://www.myswissalps.com/fo rum/topic/xmas-week-in-lucerne-2017-ideas
Other restaurants will probably close around 18:00. The Rathaus Brauerei, for example, which is my favourite place to eat in Luzern, closes on 24 December at 18:00.
>> Also, are restaurants or grocery stores open on Christmas Day in Lucerne, Switzerland?
I don’t know about restaurants in Luzern itself on Christmas Day, but the Migros grocery store in Luzern Bahnhof will be open on 25 December from 07:00 till 22:00, and on 26 December from 06:00 till 22:00.
I have been in Switzerland on Christmas Day on two occasions, and the mountain-top restaurants I have been to have always been open, as have those in the resort villages in the alps where the ski season is underway (as opposed to the bigger towns and cities).
Alpenrose