Entering the digital lotteries for Dear Evan Hanson and Mean Girls, the odds are very low you'd win that while you're in town.
In terms of the Mean Girls in-person lottery, I do have one tip. After the lottery is finished, a cancelation line will form to the right of the right most entrance to the box office. If you stake out a spot there before the lottery is drawn, you'll have a decent chance of getting an unclaimed lottery ticket (if someone wanted one instead of two), a last minute cancellation, or a standing room only ticket. They sell between 5-15 standing room only tickets per performance, depending on if patrons are utilizing the handicap designated spots.
I did that yesterday and ended up with a $30 standing room only ticket, which had an unobstructed view. The downside to that strategy is you might not know until like 40 minutes before the performance if you'll actually get a ticket.