After a No Contact order has been ruled on by a judge is it possible to be lifted before the case has been resolved?

It depends on the Judge. The judge that entered the order has the power to modify or lift that order. If the attorney representing the incarcerated person approaches the judge and makes the right argument, it might work. However, I would also advise that if the person for whom the order was originally entered is not on board with a modification of this sort, it has a snowball's chance in hell of being granted.