What is most direct train from Colmar to Lake Luzern?

It is not a question of "most direct train", there is only one reasonable route, via Basel, and there is roughly one train per hour on that route. They all follow the same route and are all equally direct.
It is more a question of what times of day you wish to travel. Trip takes about 2½ hours.

If you go to the SBB website ( https://www.sbb.ch/en ), and enter From: Colmar, To: Luzern, date: Thu 19.09.2019, time: 07:00 (for example), then click on [Search], you will get lots of options. For example:

Colmar dep 07:53, Basel SBB arr 08:39
Basel SBB dep 09:04, Luzern arr 10:05

You will have to change trains in Basel. This involves a walk of ~200 metres along the street from the French to the Swiss part of the station (the direct route is blocked by building work). I am not sure if Colmar station can sell you a ticket all the way to Luzern, because two different rail companies are involved (SNCF and SBB). You may need to buy an SNCF return ticket to Basel, then at Basel buy an SBB return ticket to Luzern.
Tickets for both trains will be valid for any train on that day.

Unless you actually want to go somewhere else on the lake, it is a big lake.

The Deutsche Bahn website is my go-to for questions like this involving international trips.

There are departures at 7:23, 7:53, 8:23, 8:53, 9:23, 9:30, 10:23, 11:23 and more. Travel time to the city of Luzern ranges from 2:07 to 2:35. You'll need to change trains in Basel. I haven't looked at a map to see whether there's a stop before Luzern from which you could board a lake boat.

The Deutsche Bahn won't show you fares (which I fear may be $$$). I'd think you could check fares on the SNCF website, but I'm not getting any results at the moment. Perhaps SBB website would be better.

Important: Although SBB's usual default is to show ticket prices paid by people holding a half-fare card (which I assume you do not have), that doesn't seem to be happening here--probably because there's also a French segment involved. But be careful on the SBB website.

I spot-checked one departure time (7:53 AM) and found a cost of 99 Swiss francs per person (about $100). I don't know whether the fare would be the same on all departures.

Hi from Wisconsin,
dbahn.com as the previous response suggested. You might have to try a couple offerings until you find their, 'search for trains'.
Excellent site, a bit clunky, give it a chance. Patience.
wayne iNWI

So, Tom Shorewood, how was the lake cruise?

I would like to hear about the train trip, too. Thanks.

@wayner - you wrote: dbahn.com - that is the wrong URL.
The Company is DB (= Deutsche Bahn = German Railways) and the website (English Language version) is: https://www.bahn.com/en/view/index.shtml

As this trip involves French and Swiss Railways, and the SBB (Swiss Railways) site is equally good, I suggested that: https://www.sbb.ch/en/