Luck is good fortune and lucre is money. As Paul explains to his mother, he had believed lucre and luck were the same: "I thought when Uncle Oscar said filthy lucker, it meant money," he says. His mother states that lucre does mean money. When Paul asks her what luck is then, she says it is what enables a person to have money. She tells him that it is better to have luck than money, because a lucky person will "always get more money."
It's not surprising that Paul conflates luck with lucre, since to his mother, the two are closely joined. Money is everything to the mother, and to her, the definition of luck is nothing more the ability to get more money. She doesn't perceive that one might be lucky in other ways. Paul internalizes her definition of luck and believes he is lucky when he can ride his rocking-horse furiously enough to discern the winner of the next race. He does not realize that the relentless pursuit of money he engages in might, in fact, be unlucky enough to kill him.