I would add to these interesting responses that "luck" becomes ironic in the novel in two ways. First, what the child perceives as luck ultimately has the consequences that we would describe as "unlucky," reminding us (as the other responded explained) that "luck" is a seductive term that suggests the positive but also embodies the negative. Second, Lawrence uses dramatic irony with the concept of luck for we the audience know quite early that the child and the family are doomed--even while the child pushes and pushes toward what he hopes are good consequences, a dream that will never come true.
He was lucky in an almost cosmic sense: he was fated, in a weird way. He had more luck than other people in the story, and indeed, than other people in life.
However, it was not all good luck, and it did not come without a price. In order to "earn" the good luck that brought the family money, he had to go into the dark places of reality. These eventually cost him his life. He was therefore very lucky--he had a lot of good luck, and a lot of bad luck.