jackets for Lauterbrunnen in June?

The issue in Lauterbrunnen at that time of year is not staying warm (it will be warm enough, unless you plan to camp out on the mountain peaks), but staying dry in case it rains... which happens often, and with little warning. A light, water resistant jacket is probably good enough. If absolutely necessary, you can augment this with a sweater.

Air temp at that location is a function of the altitude difference. The top of the Jungfrau (if you go there) is 8000 feet higher than the Lauterbrunnen valley floor and the air temp can be expected to be 25 to 30 degrees colder than the valley floor, because of the elevation difference. And it's often windy at the tops of mountains. You probably won't be outside for long at the top of the Jungfrau, but a hat and sunglasses will be useful.

Think layers. I would not bring a heavier jacket, but I would have things to layer with it. Maybe a long sleeve shirt or a light sweater to go under it and a windproof, breathable lightweight rain jacket to go over it (in case of rain.)

A sweater and light jacket is fine unless you are going to the top of the Jungfrau and staying outside where it is cold. We were there in very early June and the weather was mild. We were scared away from staying in Murren thinking that they will still coming out of the snow. This is even intimated in our RS book. Nothing could be farther from the truth. The weather was great. The wildflowers were in full bloom and the farmers were walking their cows up to the higher pastures. It does vary from year to year so no guarantees. I did put on my stocking cap and wool gloves when going outside at the top of the Jungrau.

Interestingly, I have breakfast occasionaly with a friend who's going in September. I had to talk him out of the long john underwear he thinks he needs.

We were there in September, and we just missed the snow storm that had hit a week earlier. When we were there in September of 2001, we had snow. Like most mountain areas, the shoulder season can vary wildly on what kind of weather you will have.

On our mid June Best of Europe trip in 06, we layered our clothing there. At the top of the Schilthorn where it was quite chilly and windy, we layered a short sleeve item, then a lightweight sweater or other long sleeve item, then a windbreaker style jacket. We didn't take polar fleece, too bulky, and we packed very lightly. Down in the Lauterbrunnen Valley after a good hike, our lightweight jackets/sweaters were peeled away and soon tied around our waists. The weather was WONDERFUL.
Have a super trip.

While you may have nice weather it can still be rainy anytime up in the alps. As many suggest - layering is best. T-shirt and sweater and a light weight waterproof jacket for wain that packs down is great! I love Icebreaker merino t-shirts and sweaters with a Mountain Hardwear brand Softshell and/or Pac-Lite Gortex light breathable Shell-jacket to keep the rain out. so lite and easy to toss on or back in the day pack. A matching pair of lite water-proof pull on pants are nice to have over shorts as well. A fleece is fine too as a mid layer. (I like a hat and cloves too just incase - keep them in the jacket pocket!)