Ok, it sounds like you are in a position with no intelligent adult help. I’m not clear why the coach can’t help you, but it’s true many perfectly fine riding instructors lack ground work training skills.
Apologies for thinking you are a junior. You sound now like a thoughtful adult, so I think learning basic ground skills at this stage is good.
I would stop longeing and do two things.
I would work on the ground to get him leading walk trot halt back in hand with fluency. I would carry a longe whip in my left hand to tap tap tap behind my back to get him to move. The aim is a horse that promptly moves off at your body cue and voice cue. Teach walk trottrot and whoa cues at the same time.
Then teach him to move his haunches over, turn on forehand, and shoulder in in hand with prompt response. Teach voice commands here, I like “side.” start with a finger in his ribs, proceed to light touch of whip and to just signalling with your posture.
Once you start this training you must reinforce it every second you handle him. No letting him lag behind or pull for grass.
Next, I would put him in the round pen with no longe rope, just loose. And I would get after him with a longe whip until he is going walllk trot-trot canTER and whoa transitions up and down on voice. In the process you will learn how to hold your body so that the horse continues to move or halts. You will learn how just the posture of your body is enough to signal continue moving, go faster, or slow down or halt. You will.develop your own mutual set of cues. You will learn how you can be inadvertently signalling whoa not go if you slouch or suck back or step back.
At first you may need many theatrics with the whip and you may need to run after him hitting him or the ground with some intention. I would suggest being satisfied with walk trot halt transitions at the start because we don’t know if he is fit or balanced enough for canter on a circle to be a fair ask.
Other fun things loose in the round pen is whoa (stand while I walk away) and then come when I whistle. This is useful as clicker training. Horses can legitimately be low energy but they csn also be shut down because they expect most cues from humans to be white noise they can ignore. Some clicker can get him motivated to pay attention to you.
Finally you don’t need longeng to fit up a lazy horse. You csn do it all in the saddle. So if longeing isn’t a useful tool with this horse don’t worry, just ride. Patterns and gait changes.