If Realmwright is removed from the battlefield, do the changed lands remain dual colored?
The short answer is no, they'll lose whatever type they're given when Realmwright leaves the battlefield. The reason is that Realmwright has a static ability that creates a continuous effect that dictates that the lands are of the given type:


  112.3d Static abilities are written as statements. They're simply true. Static abilities create continuous effects which are active
  while the permanent with the ability is on the battlefield and has the
  ability, or while the object with the ability is in the appropriate
  zone. See rule 604, "Handling Static Abilities."


Since Realmwright's ability is the source of the continuous effect giving the lands the specified type, the effect will end as soon as Realmwright leaves the battlefield.