With a lottery they can let people sign up for more than the one plot. If you won one lotteray, then the next roll you participate in will see - oh this person already has a plot, NEVER MIND, REROLLING.

The biggest problem system-wise I see with a lottery is that it is something the server initiates. When you try to click on a plot, the server checks then if the plot is open and tells the client whether or not it is. A lottery will have to be initiated by the server when the time is up.
A solution to that is that anyone who signed up for the lottery would have to come and check if they won or not .The first person who does that actually initiates the lottery. If it's theirs, hurray! If not, they take their money and skeedaddle. There's a short period after that for people to claim their plot or their money back. It's a bit of a hassle but it removes the responsibility for keeping track of time from the server, which would be why they wouldn't want to go there.