We will be in Lucenre for two days and would love to visit the Alps from there, maybe Eiger. Would love suggestions on should we take a tour, if so with who, can we do it ourselves via trains? Appreciate your feedback!
Thanks
Your best option would be to visit Mt. Titlis in nearby Engelberg. 45 minute train ride and trains every hour. Then you can go up the lifts to Titlis.
There are 3 local mountains from Luzern, all of which you can go up: Pilatus, Rigi and Titlis. Titlis is the highest. See website here: https://www.titlis.ch/en
Pilatus: http://www.pilatus.ch/en/
Rigi: https://www.rigi.ch/en
"can we do it ourselves via trains?" - I know of no other way. Start at Luzern station, go into the tourist office there and they will explain the details. You get a train from Luzern (or in the case of Pilatus and Rigi a boat is an option) and then a mountain railway or cable car.
As others say - Mt.Titlis. You can get to Engelberg on your own by train or you can take a tour. I think that you have to buy the tour ahead. I am not going to do that, to pay big money and then to go by a cable car into fog. If it's nice weather then I rather pay little bit more and go on my own. If it's not nice weather then I stick with Luzern.