At least there is one area where the USA airlines are indisputably the best in the world. Not to say they are perfect, but they are infinitely more useful than their overseas competitors If you think the European websites are bad, try some of the Asian airline websites, many of which feel like they were designed thirty years ago.
The LH group is absolutely maddening to deal with. You can access your flight information for any LH/LX/OS flight through any of their websites/apps, but what you can actually do in terms of managing the flight/trip info varies in wildly unpredictable ways between the six platforms, and it seems to change by the day.