OP: at least LH checked you in online for this mixed ITIN. That's more luck than I generally have. The UA and LH systems don't always play well together and I will typically need to see an agent at the airport to get checked in. Neither online checkin or self-checkin at the airport work. Luckily I can use the premier line and LH is efficient so it isn't a huge problem but they usually need to click away for a few minutes before printing the BPs for the flights.

But, yes, they see all the flights including the UA leg.