Is he familiar with any groundwork besides lunging? Can he yield his shoulders and hindquarters, back up politely, sidepass, and give his nose to halter pressure? These maneuvers can get him thinking about giving and following pressure out on the lunge as well as giving you more control on the ground. If he's too rambunctious to expect him to lunge politely and respectfully, I would start with getting his attention with those sorts of exercises first, and moving on to lunging later.
He may be pulling out because he needs more space to feel balanced and comfortable. Be sure that he has enough space to work without offbalancing or stressing his joints. I understand that you're at a bit of a space-premium, but this might be worth waiting for a little more arena space to get done. I personally use a 15-ish foot lungeline, and I also walk about a 10 foot circle rather than standing totally still. This gives my 14.1 hand horse enough room, so might be a useful guideline for you.
One more thing that comes to mind - how are you asking him to move forward? Is there a clear difference between you driving him forward and you passively allowing him to work? Sometimes, if the horse feels like you're just driving driving driving, he'll get very fast and heavy on the line. As well as clarifying your body language, incorporate lots of transitions in both gait and direction into your lunging sessions - if he needs to pay attention to you and what you're telling his feet to do, he won't get that momentum up in his brain and feet that escalates into a tough job for you.
Sorry that got a bit long... hopefully some of that was helpful to you. Good luck!