I would imagine the same issue would apply to the lottery ticket.
They’re not the same. You earn interest for every day they hold your money, so it’s schar Shabbos (although it’s only a problem when Shabbos is right next to Yom Tov, because they calculate from midnight to midnight, part of which isn’t Shabbos, so on a regular Shabbos, it’s muttar because of havla’ah).
With winning a lottery, there’s no schar Shabbos. You don’t actually earn anything on Shabbos.