I just flew EWR-ZRH-TLV, the first flight on UA, the second on LX.

I asked about an empty seat for my baby on UA and the response was something like, "sure there are seats available - the cost is $5200"

When I was connected in ZRH, as soon as I got to the gate the agents noticed I had a baby and went on the computer to find an empty seat. (They approached me before I could get to them.) When they noticed that there were empty seats, but not next to me, they paged the lounge to ask the person next to us to see if he would change his seat (he did).

On the way back, there were no empty seats so this wasn't relevant.