Connection in Frankfurt from United to Lufthansia

There is a difference between customs, control of things of value that you bring into Europe, and passport control, immigration and emigration, controlling who can legally enter the Schengen Zone.

You have two possible "checks" in Frankfurt. If your luggage is checked though on a single ticket to Copenhagen, you won't even see you luggage in Frankfurt. You will go through customs in Copenhagen, but it will probably a simple walk-thru, unless you have something to declare (rare).

However, since Frankfurt is your point of entry into the Schengen zone, you will have to go through immigration (passport control) in Frankfurt, where they look at your passport to see of you can legally enter and possible stamp it. They will definitely enter you in the database as having arrived in Schengen.

Same thing in Frankfurt when you leave Schengen. You will not see your luggage in Frankfurt. To get to your departure gate in Frankfurt, you will have to go through "emigration", outbound passport control, where they will enter you into the database as leaving Schengen.

In Dulles, you will go though US immigration and customs.

United Polaris class pax are usually entitled to all Star Alliance business class lounges, including Lufthansa

Thank you, Lee, for the very useful information. I obviously didn't quite understand the differences, and I do like to use precise language (oh, and correct spelling--I kept misspelling "Copenhagen.")