Rockoyster has linked you to the timetable. Please note his comments on the instruction page.
In particular, if there are multiple routes available, the timetable will default to the fastest one. So, to force it to show the more scenic routes, which are often slower, you may have to put in a "via" station.
Note Rockoyster's comment about a "via Kandersteg."
Besides the timetable, the other useful, in fact, necessary, tool is this map:
I have zoomed it in to zoom level "32" at which magnification the train lines appear.
Use the menus.
Under "Points of Interest, Traffic" you can turn on layers which show various kinds of transport stations.
Hotels are under "Gastronomy;" be sure to also check off "restaurants" because many have rooms. Not all are shown, but many are and it is a handy way to locate those features and others.
I note that you are traveling in June.
Weather is dependent on altitude. In June, or even May, the Lauterbrunnen Valley floor should be free of snow. (Although, the snow pack will be heavy this year). The paths will almost surely be open.
Trails at a 2000 meters or so usually don't open before June 15th; probably later this year.
So, if you want to take this easy and wonderful walk above Wengen, you may not be able to until the end of June. or even July.
Early June is the tail end of Winter at high altitudes.
This map is useful for altitudes:
map.schweizmobil.ch/?lang=en&land=wanderlan d&route=all&bgLayer=pk &layers=Wanderland&sea son=summer&resolution= 50&E=2630750&N=1161650
Luzern, at around 435 meters, will be well into Spring in May.
Wasserauen is at about 870 meters, Ebenalp at 1640.
The short walks up there can be rather steep. Early June might find them slippery, if not impassable. Late June, probably not.
This site notes that the service is closed in late November and early December, so you should be able to ride up any time in June:
www.appenzell.ch/en/al pstein/cableways/wasse rauen-ebenalp-cableway.html
In 2017 it was running from 0730 until 1800 up to June 23rd, then after that, 0730 to 1900. Every 15 minutes. I'm sure the hours will be the same; on that web site, they only have winter hours now.
When are you traveling?
By the way, a lot of us like Wengen:
The document has lots of useful information about the region, not just Wengen.