Buy your lottery tickets every day as soon as the new draw starts (somewhere close after 8:15pm NST)
Your tickets bought resets at midnight but the draw is around 8:15 NST.
So you can technically buy another 20 tickets directly after midnight and have 40 tickets for one particular draw.
But I advise against this because it only increases your chances for the one day and you will be unable to buy tickets until the midnight reset again.
Note To collect the avatar after a win you need to visit the lottery page that shows the past winners. The lottery is bugged at the moment and the avatar is only given out to the first winner listed (for shared winners). It posts the winners in order of who won first (who bought their tickets first). This is why it's important to buy your tickets as soon as the new draw starts.
This avatar can still take awhile to get but this is your best chance/fastest way to earn it.