Taking an iguana for a walk with a leash is about the same as doing it with a cat. They just don't get it. They will not follow yu, and if you give a tug to get them going your way, they are likely to panic. When they feel pressure from the leash, they go crazy, doing alligator rolls that could break their tails and spikes.
Never take your iguana for a walk on hard surfaces such as sidewalks and asphalt. One of his traits is to smack the ground really hard with his tail. That can break it at any point along it's length.
"But", you can put a six-foot leash on them, carry them outside, put them down, and let them take "you" for a walk. Even so, if they bolt, it could hurt their dorsal crest.
Have you ever let a rabbit out of it's cage so it can roam in the yard? You'll notice that they don't know how to run to get away from you. They just make short dashes. Being captive in a cage prevents them from learning to run. They don't know they can do it.
Both species can learn to run far and fast. It's better to keep them ignorant of that fact.