How big is your circle? If he's on too tight of a circle that could really hinder him in picking up a lope on the lunge, not to mention being rough on his legs in general. I don't like to use anything less than a 15 foot line (so 30 foot diameter circle) and I walk maybe an 8-10 foot circle in the center to make the radius even longer. I highly recommend some kind of leg protection (boots or polos) if you aren't already using it.
Are you in a position to roundpen him at all? Does he lope in that setting? Maybe a little more perceived freedom and space will jumpstart that lope.
As for the stopping, make sure that you're body language is asking correctly. I see lots of people yelling "Whoa!" with their voices while their body language screaming "Keep Going!". Be sure that all pressure that you're putting on him is ahead of his driveline, ahead of his girthline. Pressure here will cause the horse to stop or turn, pressure behind will drive them forward. If you use a stick or whip, I might go as far as to say drop it before you stop or switch hands with it and hold it in the hand nearer his head, so that he can't be confused about what the stick is asking. When you're ready to stop, take a step towards his head, and sort of make yourself bigger, if that makes sense. Your body language is showing your intention that he stop.
So: Trotting on the lunge counterclockwise. You choose to stop. Hold whip/neutral if applicable, even drop it. Take a decent size step to the right and slightly forward. If, looking straight ahead, you're eyes would drill a hole anywhere behind his withers you're still pushing the engine forward. In the proper position, raise your energy up, make yourself "bigger," stiffer almost. Look him in the eye, and say, long and in a low tone, "Whoooaaaa." One more thing that you might do if he plows through that is hold your right arm out, parallel to the ground, and imagine that an invisible fence is coming out from your fingertips, blocking his path ahead. The arm thing worked brilliant for my first horse... had him stopping in his tracks on his butt really well. The INSTANT his feet stop, relax completely. Let your energy fall, eyes to the ground, hand down, and praise him.
I hope that made some kind of sense and might help you out a bit.
Dennis Reis does an excellent job of showing what exactly I'm trying to convey about intentions and energy. I'm trying to find a YouTube of him... but the only roundpenning-lunging vid I can find someone put music over the whole thing and you can't hear what he's saying...
On lunging in general, I agree 100% that there should be a max of 2 circles with no transition (of gait, direction, speed, or balance. Sorry, in a Dennis Reis mood today, I guess). Horses really get burned out easily with endless circles of trot. You might look into some other kinds of NH lunging. Clinton Anderson uses a method of yielding the hindquarters and facing up into a stop on the lunge that may work better for you. The Parelli circling game does something similar, I think, and many other clinicians have slight variations that might just bridge the gap in understanding for your boy.
Sorry for the novel (E-cookies to anyone who read the whole thing and understood some particle of what I'm trying to describe), and Good luck!