I guess you could say he was unlucky because he was the younger son in the family and because his parents belittled him and preferred Richard, but it's hard to say that he wasn't a bad king as well. It seems to me that he was too greedy and ambitious and that, in addition, he wasn't a good enough politician to get away with it.
As soon as Richard was captured, John declared him dead and set himself up as king. That was not unlucky, that was dumb. Another dumb thing he did was to pick a fight with the Church by rejecting their pick for Archbishop of Canterbury and then seizing all the Church's property after the Pope interdicted England.
So it seems clear that he did some pretty dumb stuff. And it is clear that he wasn't good enough at politics to keep enough of the nobles on his side to prevent them from imposing the Magna Carta on him.