The lotto ticket achievement is obtained through a random event.

I find that events seem to happen the most when I exit the game for 15-30 minutes and come back.. if this does work, it can raise your chances of running into that event.
Also be careful about pausing the game while it's raining! When the game isn't active or you keep the detail/store or family tree screens open time will still pass by in your game and your collectibles will disappear

I hope the luck continues too!