Leads/leashes cannot be used on dolphins as intended. I have tried leashing brand new dolphins i just met, ive tried feeding them a stack of cod, ive even tried following them to treasure first and then leashing. Nothing. 

The official wiki says that "Dolphins can be leashed and be pulled around with it." and states "It is possible to leash the following mobs: -Dolphins"

https://minecraft.gamepedia.com/Dolphin
https://minecraft.gamepedia.com/Lead