I believe the problem in this situation is a dog who does not want to go to the potty while on a lead. I think what you need to do is go back to basic potty training techniques for a short period of time to unlearn your dog of not wanting to eliminate while on a lead. It should only take a few short days to a week if your consistent.

Assuming you do not crate your dog....
This is what is referred to as the umbilical cord method. The dog is tied to your waist so you can watch it every second. Then, every hour on the hour you take it outside, to the place where you want it to eliminate. I like to use the command "GO POTTY" so the dog associates the act with the command. When they do eliminate, you give them several treats and praise them like you never have before. Make the treats fantastic too! Then take them back inside, and let them off the leash for a little while.
If they do not eliminate, they do not get a treat, and they go back inside still on the leash. After a hour repeat the process again.

While your dog may be used to being off lead in the house you need to take the time to recondition the dog. Never leave it off the leash during this period (unless it's a reward) until you get them to understand going potty on the leash is an acceptable thing.

I agree that if you get Drake to potty on lead you should not have to walk him off lead (for his safety) and you won't have to worry about his habit of chasing after other animals. Especially if you walk him with a Flexi-leash.

Keep us posted on your progress and Happy Training