Jr travel card just walk up and buy in Basel? good for Pilatus lifts/train?

Elaine, the info page for Junior Travelcard the on the SBB website is here: https://www.sbb.ch/en/travelcards-and-tickets/railpasses/travelling-with-children-and-grandchildren.html
It says "you can obtain the Junior travelcard at any railway station", which means any manned Swiss station. Note there are two main stations in Basel. Only one (Basel SBB) is run by Swiss railways and that is the one you will have to buy it from. You will need their passport.
It doesn't say if you need a photo, I guess not, normally foreigners use their passport as photo ID. But if you do, there is a phot machine at the station for just such an eventuality.

"I can use the travel card for train travel Basel-Luzern and then Luzern Zurich" - Yes.
"it looks like the travelcard would entitle free rides on lifts and cogwheel at Pilatus?" - Yes. If you look at the validity map (you will get a copy of this with the card): https://www.sbb.ch/content/dam/sbb/de/infotexte/uebersichtskarte-halbtax-abo.pdf
it shows the Pilatus mountain railways as valid.

thank you. One more question. For the family card, can the adult "Swiss travel system ticket" be a super saver ticket, such as Basel-Luzern, or does it mean a Swiss Pass, etc. I assume that the family card does not get kids free rail/cable cars at Pilatus? thank you.
from sbb.ch
-Children under age 16 travel free of charge when accompanied by at least one parent holding a Swiss Travel System ticket
-The Swiss Family Card is available free of charge at attended Swiss railway stations

Elaine, now you are asking about something different, a Junior Travelcard and a Swiss Family Card are two different things.
The way I think it works (and since I live here I am not familiar with the options for foreign tourists) is:

• If you are buying a normal ticket, A to B (either full price of half price with a half price card), you buy a Junior Travelcard at 30 Franks and the kids go free.
• If you are a Swiss Pass (an option only available to Foreign Tourists), you can get a Swiss Family Card to go with it and the kids again go free.

This second option is explained in the page about passes for foreign tourists here: https://www.sbb.ch/en/leisure-holidays/holidays--short-breaks-in-switzerland/swisstravelsystem.html
A super saver ticket is just a special type of ticket from A to B. They are only available on some trains at some less popular times, and unlike normal Swiss tickets, you have to buy them in advance and commit to a specific train.
As far as Pilatus is concerned, you need to look at the map for the Swiss Travel Pass, which shows the lines up and down PIlatus as reduction only: https://www.sbb.ch/content/dam/sbb/de/pdf/freizeit-ferien/ferien-kurztrips-schweiz/internationale-gaeste/sts-geltungsbereich.pdf

So, you need to do some arithmetic and decide between 3 options:
1) Full fare tickets from A to B for each trip + Junior Travelcard (30 Franks)
2) Half fare card (120 Franks) + half price tickets from A to B for each trip + Junior Travelcard (30 Franks)
3) Swiss Pass (price depending on how many days) + Swiss Family Card (free)

If the only trips you are doing in Switzerland is Basel-Luzern, Luzern-Zürich (airport?) and Pilatus round trip it is probably option 1.
You can look up all prices on: www.sbb.ch click on the 'en' top centre for English.

thank you. I researched on sbb.ch prior to posting, but wanted to make sure I understood correctly. I assume I could also do Supersaver + jr travel pass, if we have set times? Again, thanks for your assistance.