Denny, you didn't say where you were going, but I wonder if you know that many large European airports are not set up like most U.S. airports. When you arrive for your flight home, you will need the terminal number for the building where you'll "check in". But once you enter, you'll have to find the airline and/or flight number on a big table of Check-In counter numbers. That is, they can vary how many desks each "airline" has by the time of day and the need for desks. The logos of the airline may even be "virtual", on large-screen displays over each check-in desk.
Setting aside the question of whether you printed anything out in advance, whether your seat is reserved or not, and whether you have only carry-on luggage, they will certainly want to see your passport again. (Personally, I'd want a carry-on that fits under my seat, in case you are are in the last group to board, and all the overhead compartments are already full!) The fact that you are a U.S. citizen has little effect on what the airline needs from you. The airline is under savage demands from the U.S. to provide a complete and accurate passenger manifest, a certain number of hours before the plan lands in the U.S. This is part of U.S. security checking, so checking your face against the passport is tremendously important to the airline, foreign or domestic, that sends you back to the U.S.
I've been to Europe at least 40 times, fat-cat class and Economy, and I have no idea what your "friend" is talking about. Do not get any more travel advice from this friend.
One more point-Lufthansa likely has some Codeshare flights with United in Seattle. Make sure you know which logo will be over the desk where you're going to show your passport. It could, possibly, be United or another company. I haven't been to Seattle in ten years.