April to October is peak season on the Lucerne-Engelberg-Express.
In order to take the load off high-demand trains, the operator, Zentralbahn, offers additional services from Lucerne to Engelberg and back from April to October.
Additional trains
The timetable for the additional trains can be found here (in German language only):
→ https://www.zentralbahn.ch/de/erleben/freizeit/luzern-engelberg-express/luzern-engelberg-express-s-lex-sommer
The SBB timetable is up-to-date and also knows about the additional trains.
All information without guarantee.