Just because this keeps coming up:
The Lubavitcher Rebbe told one person in a (semi) private audience that he should buy one ticket, after he asked whether he should. In no way does that show what the Rebbe’s general opinion was regarding buying lottery tickets, hishtadlus vs bitachon, etc etc. Until one knows the full back story of the individual, one can not properly gauge anything from the story
An interesting side point: In “Reshimas Hayoman” – The Lubavitcher Rebbe’s personal diary, it relates that the 3rd and 4th Chabad Rabbeim (The ‘Tzemach Tzedek’ – a famed posek – and the Rebbe Maharash) used to buy lottery tickets