I think the issue is with the word “lottery”. Lottery implies that it’s completely random (like a coin flip).
Its not random because teams can exert a fair amount of control over it by strategizing who will take them, what the goalies tendencies are etc.
As you say though the other variables such as, nerves, pressure, confidence, what has already happened in the shootout are in play.
So not a lottery as such but there isn’t as big as an advantage for the stronger team as there is in normal play.