After wrapping up my river trip in Basel I plan is to visit Lucerne on October 24 and 25 then travel by train to Zurich early on the 26th for a one day stay before flying back to the US on the 27th. What might I expect the weather conditions to be and are specific tourist attractions open or closed dependent upon to weather conditions - as an example ascending/descending Mt. Pilatus?
If I could accurately forecast the weather for next week, I would be worth a million. There is absolutely no way for anyone to answer that. The best you can do is look at the averages for those dates and realize that averages are rarely accurate since you have to have extremes - both sides - to have an average. Four or five years ago at the same time we were in that area - Zug, Mt Rigi and the weather was great. Low 70s most of the time, clear skies, no rains. Absolutely great. Would I count on that the next time, probably not.
Timeanddate.com is where I go for actual historical day-by-day temperatures and precipitation. It has data going back at least ten years, and I usually check at least the most recent five to get a decent idea of the range of weather I might experienced.
I've linked to Zurich's stats for October 2018 because Mount Pilatus isn't available. You may be able to get info on a location closer to Mount Pilatus, but I don't know whether you'll be able to find anything about conditions at altitude. I think the usual advice is to take a look at webcams early in the morning and make your decision then.
You will probably need a coat. It will be unlikely there will be any snow in Luzern, though plenty on the mountain tops.
It may rain. it will be windy out on the lake.
This year was exceptional, summer went on for ever, clear into early October, then went colder fast (normally starts cooling early September). But this autumn, who knows?
I have never known snow in the lowlands (Basel. Luzern, Zürich) in October. Sometimes snow in late November, then nothing until after Christmas.
Temperature changes a lot with altitude, You will need to wrap up warm going up Pilatus, Rigi or Titlis.