The lottery should be for the top 4 picks (worst 4 teams). You could also break it in to pods.
4 worst teams draw for top 4 spots. next 4, next 4, next 4. This way the draft benefits the teams it should. The team who finishes dead last should not have to suffer by getting the 6,7,8 overall pick. You could also adjust the pods so that the top two teams auto get the last 2 picks. Top 4, next 4, next 6.