"Does renting a car make sense to do that or is it just as easy by train?" - No , it is easier by train. Trains go where cars don't, and you get to look at the scenery without risking driving off the road, and Gimmelwald, Wengen and Mürren are only reachable by train, no cars.
Are you saying you are staying in Zürich, and doing all these places as day trips (Luzern, Lauterbrunnen, Gimmelwald, Wengen, Mürren)?
Or are you saying you are arriving in Zürich (airport?), immediately moving on to Luzern and doing the rest as day trips from there?
Staying in Luzern is better than staying in Zürich. Unless you have a good reason to stay in Zürich.
Even better to split it, staying in Luzern and move on to stay in the Berner Oberland.
Lauterbrunnen, Gimmelwald, Wengen, Mürren are all within a few minutes travel of each other. They are actually close enough to walk from one to another, if you don't mind going up or down as much as horizontal.