In the last 25 years, I've flow into MUC three times and out five times, but I haven't used the airport since 2013, before the T2 Satellite was built, but I have studied the website to try to figure out what I might do in the future.
Go here to see a map of the Munich airport. G and H gates are on different floors in the original Terminal 2 building which is connected to the new satellite building, gates K and L, via separate underground shuttles, one for the Schengen zone (G and K) and one for the out-of-Schengen zone (H and L). I believe there are immigration check points in each building. I think both immigration and the shuttle access are in the middle of each long building. You can go between floors in a building and between buildings entirely within one security zone.
I looked at the arrival and departure information for your flights for a typical day in the near future. Gates, of course, can change. On that day your flight from LAX was arriving at gate H48, which is at the extreme southern end of the original T2 building. Your departing flight was from an unnamed gate on the K level of the satellite building. On arrival, you should proceed to the middle of the building where you could go through immigration, then go down through the G level to the shuttle station and take the Schengen shuttle to the K gates in the satellite.
Alternatively, you could stay in the out-of-Schengen zone and take the shuttle to the L level of the Satellite and go through immigration there to get to the K gates.