Hello Wheembeengou18
Hello
For the first day, you can buy a point-to-point ticket from Basel EuroAirport to Interlaken Ost or a Saver Day Pass if it is cheaper. Don’t buy Supersaver Tickets, your flight could be late and you could miss the planed train. Be sure to buy full fare tickets, the first displayed price is always the half fare price.
For the third day, I think that a Saver Day Pass (full fare) will be the best solution. It is valid until Chiasso (border station). The online timetable will always show you all available prices.
You can also find the price of the Saver Day Passes for the days of you travel here:
https://www.sbb.ch/en/tickets-offers/tickets/day-passes/saver-day-pass.html
From Lucerne, you change normally in Lugano and take a regional train (RE 80) to Como. You must buy a separate inexpensive Arcobaleno Transfrontaliera ticket from Chiasso to Como S. Giovanni. The ticket is valid four hours, chose the timetable of the right train from Chiasso to Como. This ticket is not valid in the Eurocity.
For the second day, you should choose another destination as Lauterbrunnen, the principal touristic attractions of this village are the car park and perhaps a souvenir shop. You could take the cable car and the train to Mürren or choose another destination in the region (for example Grindelwald with the train). It is not necessary to buy tickets in advance, you can wait until you know if the weather is good or not.
Kind Regards
Daniel