There is a lunging system I used it on my pony who has just been broke
if that doesn't help^^, try the pessoa system
There might be different reasons why horse doesn't want to lower and strech their neck. Horse might be unbalanced, distracted, fresh or not steady.
What I do with such a horse is I do a quick warm up on both reins and then put side-reins on. Usually, the length of them should reach to the horse's pole when its stood relaxed with its' head straight.
During trot the side-reins should encourage them to go into "contact" and lower their head. This is because the side-reins are sending vibrations to the horse's mouth just as if you were riding it.
Also, as you're lunging, you pull the lunge and realise. You start gently but if the horse still does not stretch down you pull more and less gently. Sometimes shorting the side-reins will help. Make sure they are not just hanging.
Remember to keep the lunge whip pointed at their shoulder to keep the horse on the circle and so its not coiming inside of it.
Keep the horse going forward in a good tempo and rythym to keep it balanced.
Hope that helps :)