About 10 mins each direction. You keep lunging your horse (if he's hot and not listening) until he softens and is responsive. But don't overdue it. When he listens and does what you ask give him praise, when he's naughty stay calm and keep him going to show him you're the leader. Hope that helps!
I lunge mine for 30 minutes, but to stop it getting boring I add a lot of changes of direction and add some jumps to make it more interesting for them. I have lunged for longer but only on cooler days.