Where is this nitpicky guilt even coming from?
(Spoiler: maybe from the history of your childhood)
Lottery thing is not anti-capitalist in its nature to begin with
Not everybody would even buy a lottery ticket. Plus you're not taking any money from people with lower income than yours. I mean is this from the country budget? As far as I know, it's not.
I think if everyone will be this way then lots of people will find lots of these super small and often totally insignificant things to feel guilty about.
I can understand feeling guilty about buying things made by slave/exploitative labor (it should be less guilt, but more doing stuff about it to end it cause it's often even not avoidable). But I don't think you're exploiting anyone with the lottery. You haven't even won yet!