I'm UA 2.5MM (lifetime *Gold) and recently made an award booking in economy FCO-MUC-ATH on LH. I was automatically allocated seats on these LH flights. However I decided to change the flights as I found a more convenient schedule on LX. To my horror I found that I no longer had assigned seats and had to pay at least EUR 10 per sear per segment.
Makes you wonder why LH's little sibling is so much less obliging and whether they should be a full Star Alliance member at all. I'll remember how poor LX is compared with LH the next time I make a booking.