Munich airport

You will go through customs in Rome.

But you go through immigration in Munich.

You are obviously confusing "customs" with "Immigration". Customs is checking for goods being imported, and if you have nothing to declare, you just walk out the "nothing to declare" door after you pick up your luggage at your final destination, without delay 99% of the time.

Immigration will be where they check and stamp your passport and allow you to enter the Schengen zone of Europe. That will take place at your point of entry, which in your case will be Munich. You could be in line waiting for this to happen. Your inbound could also be delayed. Just know that Lufthansa has 5 flights a day going to Rome, so if you did miss your flight to Rome, chances are good that they will get you on the next flight.

I had a similar short layover in Munich in Sept ‘22. I was not convinced I would ever make that connection, but everyone told me that in Munich it would work fine. I was arriving two days prior to my tour so I knew “if the worst happened “ I would still be okay if I was delayed by a missed connection.

Turns out that I went through passport control, used the washroom, and still ended up at the gate for the next flight before they started boarding. It was amazingly fast.

There is every likelihood of making this connection, but make sure you are flying with a few days buffer between your flight and any “must meet” deadlines.

I flew Lufthansa from Vancouver to Venice once a few years ago, and also went through Munich. I had an hour to make my connection. I seem to recall it was mid afternoon in Munich so that might be why the crowds were so large, but the moment I walked into the large room where everyone was lining up to go through security I knew I might be in trouble. There was really no indicated lines to guide people to the security screeners, so people were just gathering in large groups, and there was no staff in sight to ask for assistance from. I saw more than one panicked looking traveller that day. By the time I got through security, then had my passport stamped, I could hear my name being called on the PA. So, I ran, right past the gate I needed, which was hiding in a corner, and bolted up to the first person I saw at a counter in a Lufthansa uniform and blurted out “ they’re calling my name!” Fortunately, she understood, I told her what gate I needed, she pointed me in the right direction, and made a phone call to let them know I was coming. I made the flight, and I wasn’t the last person to arrive in a panic. One other woman came up right behind me. So, don’t dawdle when you get off the plane, and if you encounter a long line to get through security then look for a Lufthansa employee to help you, they may be able to at least get you to the front of the line.

Customs vs immigation was discussed.

Even for immigration and transfer of flights "only" the 50 minutes are a narrow timeframe.

I don't know why Anita had to go through security as described above. You should not have to deal with any security lines, just passport control then on to your connecting gate.

I was also surprised Sam, and the first time I walked into the room with the crowds waiting for security I thought I was in the wrong place so I backtracked but couldn’t see where I had gone wrong, plus everyone off my flight was in the line for security so I just got in line.

There was certainly no need to go through security when I transferred flights. I don’t think you will need to.

If in doubt, talk to the people in line around you. My experience--in airports everywhere--is that if you are panicked, people will let you through.

In Toronto last summer, I came up to a line in tears trying to get to a funeral and having been delayed by climate activists gluing themselves to a runway, a rebooking, a medical emergency on my next flight that delayed deplaning, and having to pass through Canadian customs despite having no idea where my suitcase was and never intending to enter Canada. The lady in front of me simply yelled, "Hey everyone, can we let this lady through?" and EVERY PERSON in that 100 person line let me jump straight to the front and one lady gave me tissues for my tears and another guy pointed me to the fastest security line. I made my connection (which was then delayed due to a bird strike and my suitcase came a day later). I have let people through and been let through in airports everywhere.

You should be fine, but if there is a line, simply start talking to people! Most people are really awesome.