transfer from Basel to Lucerne

There is a train from Basel station (Basel SBB) to Luzern ever 30 minutes. Takes between 1h and 1h30 depending on train.
You can look up times and prices on the SBB website: https://www.sbb.ch/en

There are 3 different places in Basel ships dock: St Johann, Klybeck and Dreiländerecke. The easiest option is to get a taxi to Basel SBB station, which will cost about CHF 25-35. Then buy tickets (cost CHF 34 per person) and get the next train to Luzern.

As always, if you are travelling by train you need to carry your own bags through the station, onto the train and stow them on the train yourself.

with 4 people it will cost about 134 swiss franc- do you think a shuttle or a drive would be more economical?

pecanlady, I am not sure what you mean by "shuttle or a drive" other than a pre-booked taxi. That would be a lot lot more expensive. Nobody really does that in Switzerland, as train is the normal method of transport. Except perhaps for US-Americans who choose that method of transport as that is the system they are used to in their country.
I did a Google search, and I came up with a number of companies. The only one that would give me an estimate from the website quoted CHF 320 for 4 people in a car.

Since you know the day you are getting off the ship, and approximate time, you can get Supersaver tickets. They go on sale 30 days before the travel date and you can often get the tickets for 50% off. Since they are nonrefundable and paid for ahead of time, and you must travel on the exact train you bought them for, leave plenty of time from when you expect to get off the ship. Plan on spending a few hours touring Basel before you schedule your departure to Luzern.

https://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/supersaver-tickets.html

For instance, right now, looking at Feb 24, they are 17 CHF per person for the 1:04 pm direct train to Luzern which gets there at 2:05 pm.

Hiya - I took an Avalon River cruise that ended in Basel. Our cruise director coordinated taxis for everyone who wasn’t going to the airport. We had to pay the driver of course for the trip to the train station. I don’t remember how much it was, reasonable I thought. I would assume Viking will do the same. I stressed over the situation too, even posted a question here and “Chris from Basel”replied helpfully as always. It was really so easy. I also recommend staying in Basel for a few hours, it is worth a look! We just stowed our bags in the lockers, took off on a tram, saw some sights and then went back to the train station to leave Basel. The square by the cathedral is really pretty. Lucerne is lovely, are you connecting through Bern? I really liked Bern as well.

Bern is quite a bit out of the way going from Basel to Luzern. Of course, the OP has not said what the rest of the itinerary is.

You are right! “Connecting” was not the right word choice, oops. Bern would have to be a separate stop on the itinerary.

Hi pecanlady, we did the Rhine Getaway cruise with Viking Oct 2017. The cruise line was great and pre-arranged taxis for anyone who needed them. Take a taxi from the ship to the train station then train to Lucerne.

Viking also has pre and post tour options. The Lucerne extension is 2 days for $599 and includes a walking tour. Viking will arrange your transportation and hotel if you choose this option. Check it out!

Donna, that's $599 per person. For 2 nights, that's not exactly a bargain.

Hi Stan, I didn't say it was a bargain but it is an option for the poster.