As for the issures with leading, here is a good video that I always recommend:
And a couple of articles to read: Training Your Horse To Lead - Part One
and for a slightly different approach, Leading a Horse For Respect
As for the lunging, are you lunging in an open area or a lunge arena/round pen? I find the best for coming in is for your horse to first be fine walking correctly at the correct distance away from you when lunging. I use my lunge whip for this. If my horse starts coming in, I move the whip up to point at their shoulder and say "out", firmly. Once they have moved back to where I want them to be, I return the whip to its usual position behind them.
As for the laziness, I can hazard a guess at helping though I have the opposite problem with my horse. I like to follow the "ask-tell-demand" set up. I ask my horse to trot on by simply giving the voice command of "trot on" - said in an energetic way. If she doesnt trot on, then I flick the whip once or twice behind her. If she still doesnt trot on, then get dominant on her. Crack the whip, flick it across her hindquarters, anything to get her moving. And then, only let up when she is moving out nicely, not a slow trot, a proper trot! I know it will seem like a pain because you'll have to do it a lot but if you're consistent and get on her case the moment she slows down, she should learn that its your way or the highway.
For the last problem, getting her to stop and turn her around. I like to teach the "whoa" command when I am leading first. (I teach "whoa", "walk" and "trot on" on the lead first before lunging). Everytime you stop while leading her, say whoa. The trick with word commands, or at least I've found it to be so, is to say the word with lots of energy when getting them to move up a pace, and then to say it slowly and calmly when getting them to slow down. Once she knows the voice command, and since she is a lazy horse, she should be easy to slow down on the lunge. Get her walking, then say "whoa", I lower the whip to the ground, look down at the ground and 'take away' my more assertive, driving body position. My mare then stops and faces me. I then approach her, give her a rub on her face and then ask to go around the other way.
Getting her to go around on the other side, the best way is to get someone to help you and lead the horse around (from the ground is fine) while you're lunging on that side. I unfortunately did not have that luxury when my horse refused to go around to left. So this is how I did it: My mare had the habit of turning in to face me and backing up instead of moving forwards when I asked her to go left. So standing quite close to her, I opened up my left arm, gesturing with the lunge line which direction I wanted her to go and said "walk on". When she backed up, I started gently flicking the whip and kept approaching her, moving the whip more and more. I eventually had to flick her with it on her hindquarters until she moved forwards and then I dropped the pressure off, and gradually let out the line until she was making a 20m circle. I had to do the same thing about 4 more times and since then she is fine with lunging on the left.
Sorry for the essay! Hope it helped!