It takes a lot of people to play a lottery or there won’t be enough money to make the prize worthwhile.
Lot is from the word lottery, a very ancient practice from a time when people cast marked pebbles into a pot and then selected a winner through a draw.
To “throw in your lot” with the others meant you had joined them in the gamble.
A lot, meaning a large quantity, took its meaning from the many balls or entrants in the lottery pool.