Thank you rjque. I think we'll end up getting the extra seat, especially if we decide to travel in September, when our son will be 14 months old (probably too big even for Lufthansa bassinets). If we buy him a seat, we'll have a few extra options to consider, e.g. Air France and KLM: they are somewhat more expensive but fly to SVO instead of DME, which is more convenient for us. I guess their service is better than United's one, too.

Our child slept well in his car seat until recently, but now he is curious about what is going on around him. However, things may (and probably will) change by the time we are going to travel. I doubt that he will be able to sleep in a coach seat though.