Almighty God allows what He allows. His reasoning, if it can be called that, will only be known to us in the next life, and even then, only insofar as He chooses to reveal it to us. So, yes, a traditionalist Catholic could win the lottery, or he could not.
I can only say that if I ever win it (i.e., win one of those multi-multi-million jackpots), I can think of one city that will have a very nice traditional Catholic church, with resident priests and solely the Latin Mass available on a daily basis, and ownership and all financial matters will be overseen by a corporation and board of trustees selected by me. Depending on the amount of money involved, a free K-12 traditional Catholic school, with quality instructors both lay and religious, reflecting the diversity of the Catholic community (i.e., not just for rich people), would also be created.
And I might buy a somewhat bigger house and a new car, set up a trust fund for my son, and arrange for high-quality in-home care for my elderly parents. That's about it. I live simply and wouldn't know how to live otherwise.