I am working a greenie lazy right now too. I started lunging in the round pen with side reins not real tight. Side reins can be your choice of course. I would do tons of transitions from trot to canter and back down and halt, and switching directions alot. Not for a long period of time but enough so if he slipped and got off balance he didn't kick out or duck. Then after a few weeks I got on in the round pen. We started with me having to whack the reins on him, not hard but enough to get his attention and shift from the fast trot into canter. I let him do about half the round pen and stopped. Then went the other way and then quit for the day. I did this for a week or so. The moved up to the whole round pen. Now I can circle around it no problem. We have just moved to the big arena in the same progression, ask for lope, lope 10 strides. Quit. We will work up to the rest. Some horses it's just harder for them to learn to balance. My round pen is 60 also, plenty of room if they can learn to balance.