Train from Brig to Lauterbrunnen

I don't know where you are looking, but there is at least one train per hour one every line and at every station in Switzerland, so there is absolutely never a 3 hour wait.
Look up times on the Swiss railways site: http://www.sbb.ch/en/home.html

Enter Brig to Lauterbrunnen, and your desired date and time.
But, if you are coming from Milan (and, I assume, you will already have a ticket from Milan to Brig as well as your Swiss rail passes), just enter Milan to Lauterbrunnen. The trains from Milan do not terminate to Brig, they carry on further. Depending on where it is heading to you may not even have to change at Brig.

P.S. If you are coming from Milan, your Swiss Pass is actually valid from Domodossola, which is before Brig. So you only need to buy a ticket from Milan to Domodossola.
See the Swiss Pass validity map here: https://www.swisspasses.com/railpass/overviewmap_en.pdf

When I look at the website of the company that runs the trains, SBB, for which Chris gave a link, I see 2 trains every hour with a 7 to 9 minute "layover" in Spiez and a 7 to 8 minute "layover" in Interlaken. I hope you're not using RailEurope's schedules.

Stay away from RailEurope. One of its many faults is to not show you the full array of available trains.

As the others have mentioned, as you have Swiss Passes you only need to buy tickets from Milan to Domodossola. It would help to have some idea on which train you're planning to take, and on which date?

For the trip to Lauterbrunnen, you will always have a change at Interlaken Ost, where you'll transfer to the small Berner Oberlandbahn for the final 20 minutes to Lauterbrunnen. Be sure to check the small digital display on the side of the car, as some trains split at Zweilütschinen. It's a scenic trip so have your camera ready.