Hi, and welcome to MySwissAlps!
Are you doing the reservation on the HappyRail website? It doesn't seem to me that you can reserve anything except the full route on that site, but I will leave it to others to confirm whether that is in fact the case.
You can reserve Göschenen to Flüelen on the Gotthard Panorama Express in the SBB Ticket Shop, and I can give you instructions for that if needed, but first of all I would suggest you consider whether or not a reservation is worth it. You can travel over the same route by normal trains without a reservation. Reservations are actually not even possible on the normal trains.
You can't reserve the boat from Flüelen to Luzern, so the reservation would only be for the rail sector Göschenen to Flüelen. This is a 41 minute trip, and a reservation on the Gotthard Panorama Express would cost CHF 12 per passenger. In my view, the most spectacular scenery in this area is the Schöllenen Gorge between Andermatt and Göschenen, which you will have already passed before getting to Göschenen and joining the Gotthard Panorama Express; and the area around Wassen, where the train negotiates a series of loops to lose a lot of height within a very short distance.
When you get to Flüelen, you can get a boat to Luzern whether you are on the official Gotthard Panorama Express or not.
If you want to take a boat from Flüelen to Luzern, you will need to do separate timetable searches for Zermatt-Flüelen and Flüelen-Luzern, otherwise you will just get the fastest connections from Flüelen, which will be trains. For searching the timetable for the sector Flüelen to Luzern, use advanced search to limit the transport options to "ship".
Attached are screenshots from the SBB timetable showing an example of how you could travel on the Glacier Express from Zermatt to Andermatt, then from Andermatt to Flüelen on a normal train without reservations (same route as the Gotthard Panorama Express), then from Flüelen to Luzern by steam boat. You will arrive at Flüelen a few minutes before the Gotthard Panorama Express does, and end up on the same boat as its passengers will.
My screenshots are from the old version of the SBB timetable, which I prefer for both content and presentation. The link for that is