Round-trip United award reservations allow 2 open jaws and 1 stopover. As we saw when booking free one-ways on round-trip Delta award reservations, we need to use one stopover and one open jaw to book a free one-way: the stopover in our origin city, then the open jaw to the destination of our free one-way flight. You can use the other open jaw however you like.
Fortunately, United's booking engine actually works, unlike Delta's, so you can price out and book a free one-way ticket simply and easily online. Here's a sample search for Chicago (a United hub) to Frankfurt (a Lufthansa hub), plus a free one-way flight to San Francisco at the end:
Notice that our later trip to San Francisco has nothing to do with the original roundtrip itinerary to Frankfurt. It's a month later. But sure enough, this prices out in Business Class just like a roundtrip without the one-way flight to San Francisco: 100,000 miles plus taxes and fees.