Hi Fandi -
Welcome to the forum.
The following services all run on Christmas Day, and run in both directions (to or from Luzern/Rigi):
Lake boats from Luzern to Weggis or Vitznau;
Trains from Vitznau or Arth-Goldau to Rigi Kulm;
Trains from Luzern to Arth-Goldau;
Luftseilbahn from Weggis to Rigi Kaltbad (connecting to the train from Vitznau at Rigi Kaltbad and onward to Rigi Kulm via cograil.).
There is a nice walk from down Rigi Kulm (or Rigi Staffel) to Rigi Kaltbad via Rigi Staffel Höhe and then swinging out to Chänzeli for a good overlook before continuing to Rigi Kaltbad ( passing the small chapel set back from the trail on the left near Rigi Kaltbad.)
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The connection between the boat and cable car (die Luftseilbahn) at Weggis requires a significant walk uphill from the boat dock to the valley station (Talstation) of the Luftseilbahn. . Approximately 700 meters distance, with a climb of approximately 65-70 meters. The timetable shows 15 minutes. I think it takes longer. There is no shuttle bus. Personally, I'd prefer to make the walk downhill. ;-)
An alternative is the ride the boat from Luzern further to Vitznau and catch the cog-rail train up to Rigi Kulm. Nice views. Sit on the left.
Sources for details -
Altitude change in Weggis - approximately 65-70 meters:
map.geo.admin.ch/?X=209772.00&Y=676218.0 0&zoom=9&lang=en&topic =swisstopo&bgLayer=ch. swisstopo.pixelkarte-farbe
I cannot offer and firm answers or comments on which restaurants or hotels or are open on Christmas day. I'd guess that most will be. However, the tourist information office by track #1 in Luzern Main Station probably can help you with that information. They are very knowledgeable.
However, if there is snow, there will certainly be skiing.
I hope that you have sunny weather. The views are quite nice, particularly from Rigi Chänzeli. (Also spelled Känzeli.)