You need not to worry about reaching Mount Titlis from Lucerne if you are experiencing your Mount Titlis Tour with Thrillophilia. Just reach at the meeting point and they will take care of the rest.
However, in case you are organising your own Mount Titlis day Trip, then you need to catch Lucerne-Engelberg Express which will ride you until Engelberg. From this point, you will find various buses plying to the cable car ride which you shall use to reach the starting point of it. From this point, you can catch 8-seater Titlis Xpress Gondola Cable Cars which can easily fly you up to the peak of the Mount Titlis.