That discount won't use a travel day, don't worry. You can buy half-fare tickets on the boat company's website or on sbb.ch/SBB app. 

Staff should know that Eurail gives a 50% discount but feel free to show them that too:

From https://www.lakelucerne.ch/en/your-cruise-experience/timetable-fares/faq/various-questions-1/

Depending on how far in advance you book it might be cheaper to buy a (1st/2nd class) full-fare Saver Day Pass for the whole day trip. It includes the boat and the cogwheel train to Rigi.

Many thanks for your reply thibcabe.  Understood.  Part of my question concerns if I could travel on the boat 1st class while I will be using a 1st class eurail global pass. Might be a mute point but seeing the boat company allows 50% off using the eurail pass, will they allow me to travel 1st class, or would I have to pay extra to upgrade to 1st class?

Bob

If you'd like to go 1st class on the boat you need to buy a 1st class ticket for the boat trip (which is more expensive). It will cost CHF 24.

If you do buy a (cheaper) 2nd clsss ticket for the boat trip, you are only allowed in 2nd class even if you do hold a 1st class railpass. It will cost CHF 15,50.

For both boat tickets you do get 50% with your railpass (prices given are with discount).

Thank you Hektor for your kind and full reply.  Yes, just as I thought, the boat company’s not giving anything away.   The reason for going 1st class on the boat (especially outbound from Luzern), is that I have read the boat 2nd class can be quite crowded in the early morning sailings in Summer.

Buying the Day saver pass for the day may well be the answer.
Regards Bob

Hello Hektor.  Just a further question re the 1st class upgrade on the boat.  Is the price of CHF 24 you mentioned one way, or round trip please? Regards Bob

A further question re Lake Lucerne 1st class boat trips:

If I buy a 1st class DAY SAVER pass & travel on the boat from Lucerne to Vitnau, would I be allowed to travel in 1st class on the boat?   Or would I have to buy an upgrade to 1st class.   Bob

No, this one is valid without any supplement. Be aware that a day saver pass might get expensive if not bought in advance (e.g. for Thursday it’s already 178 CHF); but I assume you did have a look.

re package deal for RIGI inc 1st class boat,

I found a package deal for Mt RIGI on the SGV boat web site that includes 1st class Lucerne to Vitznau & return, use of RIGI trains and cable cars, and a visit to the Mineral baths and Spa which my wife wants to do.   My question has to with pricing:
On the SGV site:

webshop.lakelucerne.ch/en/

Click:“Cruises and mountain excursions   See all”

Click on “package - Mineral bath RIGI Kaltbad & boat”,

Click on:  “Book a package”

Click:  “Package with RIGI Day Pass”

                                      “Add ticket”

When I fill in the details of the trip with my name,& after clicking on the “Ticket category” box, I was wondering what I need to check next, while holding a 1st class eurail pass:   Do I check the Half-fare Card box, or do I have to check the Adults (16 years +) box?
In other words, is the eurail pass considered  a Half fare card?

Replies appreciated.  Bob

(There are two prices: CHF 102.80 & 153 showing)

I think you can indeed check the "half-fare” box, since that normally applies to anyone who qualifies for 50% discount.