To me, frugality is an attractive mode of thinking that ties in with self-discpline, ethics, and making conscious and rational choices. This can be healthy but has also lead me to live and think in unheathly extreme frugal ways (at least when I was younger and didn't have kids to be responsible about).
More generally, frugality is (to me) just one aspect of optimising my life and maintaining mental and physical health. For instance, the lottery example boils down to this: how can the extra money make you more contented? Does it in fact make any positive difference? An old man near where I used to live turned down a million-dollar lotto prize, presumably because he already liked his life as it was. In fact, studies have shown that winning lotto prizes actually leads, on average, to less happiness.
I would spend almost all of the lotto money on trying to make the world better, but keep about $1M for ERE-type purposes. It would be very important to keep up the frugality and, even more importantly, to keep up work of some kind, paid or not, that could do good and give purpose, pride, and satisfaction.
All in all, free money wouldn't do much: $1 or $10 or $100 is nice to find on the road but it makes no difference as money. $1000 or $10000 can buy you some toys that you don't really need and could afford anyway. $100000 or $1M would give a good ERE-type investment sum/buffer; I wouldn't mind those amounts. $10M or $100M could do some good in the world on a small and local scale but not much, so I wouldn't be very interested in these sums. $1B or $10B could maybe have some tiny effect on the world, and $100B could actually fix a few world problems, so I wouldn't mind that money. However, even these sums are pretty trifling though: even Bill Gates or Warren Buffett don't have any "real" money, at least not to fulfill any sort of grand dreams, like a trip to Mars or even the moon, so even their riches are more like bling than substance. All in all, there's no realistic level of richness that could really fulfill you or realise your dreams... unless you have sad and bling-full dreams