currently stalled 24/7 with free choice hay and grain three times a day.
Why is he cooped up?? You won't get him in great shape if he's stuck in a stable 99.9% of the time & will also likely suffer more/sooner from stiffness/arthritis, sore/poor feet, etc, due to being kept locked up. Get him out into a paddock for some free movement pronto, before working him, or if you can't, take him out for walks a number of times daily at very least. Why is he fed grain? What type?
My question is, should I be treating him like an 'old' horse? He was lunged for a good 20 minutes before he even broke into a sweat,
Yes, given his poor management, not his age, I'd go very gradually with any high impact stuff, tho as above, the more low stress exercise you can give him, the better all round. I would not be doing much lunging with him for a while at least - circles are hard on joints & running endless circles until the horse gets sweaty is too much. I'd use the lunge/roundpen for training purposes rather than exercise, & stick to walking & trotting.
Whenever he tried to stop in the round pen and eat, I made him work harder for a minute or two to get the message across. What can I do to get him to pay attention to me more? He's very sensitive to the lunge line, and I barely have to flick it to get a response, but he loses focus quickly. I try to correct him whenever I'm leading him, but with him so sensitive to any rope movement, it's a little hard to do in close quarters.
Firstly, horses need *instant* feedback & don't associate What Happened Then with What's Happening Now. So with your working him harder as a consequence of putting his head down when he feels like it, get after him immediately, but don't persist with the correction - 2 seconds is bordering on too long for him to 'get' that it's punishment, let alone 2 minutes. Also don't forget to reinforce 'good' behaviour by quitting the pressure/work &/or rewarding him with Something Good. This is partly why I don't like lunging just for exercise - the horse does endless, mindless circles & mentally switches off, gets bored, gets frustrated... - especially a horse that's been left for however long & you're unsure of his training & haven't yet developed much of a relationship with him.
What you describe as 'very sensitive' sounds like he may be reacting out of fear to the whip/rope, rather than responding with trust & understanding. This may be that he was never taught in a way that encouraged him to trust & understand his handler & their tools, so you may need to start at square one, or it may be due to him not having learned to trust/understand you
yet. Either way, I wouldn't be trying to elicit responses with a stick/whip until he learns to trust it & you, so he can learn to *respond* rather than react. If you can't ask for a few steps at a walk, IMO you have no business getting the horse cantering yet. Doesn't sound like I'd be considering riding yet either. Hope that made sense & helps!