I often get asked why it's so hard to potty a small dog on lead. They sniff and sniff until you feel they know every blade of grass on a very personal basis, yet they won't go. Then you decide that they don't really need to go, come back inside and -- boom-- they do their business right there. What's with that?
I think it's important that you realize how much you communicate to your dog through the lead. If the lead is tight or you are jerking them in any way from place to place, realize: I am telling my dog that he must be under my control and do what I say. And just like we like to do our business in a quiet, unstressed environment, so do our dogs.
So first and foremost, loosen up. Loosen your hand on the lead. Go to where you want your dog to go. Stop. Become a post. Let your dog walk round you, finding the right spot. Watch the pretty clouds. Or an interesting tree. Pretty soon, if he needs to go, he will squat. Then praise. Continue this until he looks like he's done. Then take a nice walk. You don't want to head straight back to the door as soon as he's done because that tells your dog that the longer he holds it, the longer the walk will be.
This way pottying on lead can become a regular and happy routine.