Lauterbraunnen to Murren: hiking uphill as alternative to aerial cable car?

I hope they're in good shape. It seems to me to be about 1000 vertical feet straight up and about 45 degree angle.
Edit. Blow it up on Google maps and you'll see a switchback trail designated "Alpweg".

It's about 2,300 feet of vertical elevation gain. Starting elevation about 2,600 feet above sea level and the Grutschap station is almost 5,000 feet above sea level. That's a lot of elevation gain.
Especially hauling significant weight on your back.
You'll probably want to do what Sam suggested, it's easy to take a look at the route. Just my quick look suggests the mileage could be significant, because of the switchbacks.
With Google Earth you could actually measure the mileage, which might be a good idea.
I have not done this and have no personal experience on that route.
There's probably a reason they built the aerial tram.

jay,

I vaguely recall a small road twisting back and forth under the Cable Car, but as the others have mentioned there are many switchbacks and it would probably be a somewhat strenuous hike (especially if the person is hauling their luggage with them, LOL). The Cable Car trip only take about 10 minutes and it's not especially high (unlike the trip to the Schilthorn). THIS is the approach to the Grütschalp station.

My suggestion would be for your friend to close his eyes and just tough it out for such a short ride.

It is trail 51 and here is the description (in German). They say 3 hours from Lauterbrunnen to Muerren. Of course, 2 of you can haul all the luggage to Muerren station easy enough, and 2 others can hike. You did say you going there to do some hiking.
http://www.jungfrau.ch/uploads/media/51_52_Lauterbrunnen_Alpweg_Winteregg_M%C3%BCrren_03.pdf

I've hiked part of it. Nothing particularly difficult in terms of technique, but you need a fairly good baseline of physical fitness.

I understand being nervous about taking the aerial cable car. If it's just a standard fear of heights that you're dealing with, then my strategy would be to stand in the middle of the car, not near the windows, preferably with all your friends gathered around. Travel time is only 4 minutes.

The person afraid of heights can hike. The other 3 will be waiting for him/her at the bar at the top.

My wife didn't like the idea of the cable car to Murren but she just stared at the floor and dug her nails into my arm and it was over pretty quickly. And to her credit, she kept going all the way to the Schilthorn (and back, natch).

The cablecar from Lauterbrunnen to Grutschalp is not that far off the ground. It parallels the slope up, just above the old funicular path.

The Schilthorn cablecar, on the other hand, can have you dangling over thousands of feet of air, so not pleasant for one with a fear of heights.

Gondola from Lauterbrunnen to Grutschalp just barely hovers over the tree tops. Don't like heights...then don't look. Although you'll be missing the most beautiful views in the world.