I don't know anything about Messi's situation but I am very familiar with growth hormone deficiency.
My son was diagnosed at 3 after testing for many things as he was not only very small, but he missed his milestones and was getting every therapy imaginable. At the age of 15, after a bone age scan in his wrist we stopped taking it.
The protocol is to stop for 3 months and take another stim test, similar to the one he took at 3, to determine if the patient is producing enough on his own for metabolic processes. Most patients produce enough on their own. Although the test seemed to go well with cortisol levels and insulin levels behaving normally it was determined that my son didn't produce any on his own and needed to go back on it for the rest of his life.
Instead of 1.8 every night he takes .8 three days a week. He'll have to inject this on his own and find a medical plan that covers it as he gets older.
We know a few other kids who are on it, they started at the age of 13 because they were short. One was always very short but was a great athlete (perhaps like Messi?) and the other just stopped growing and his younger brother got taller than him.
Without GH I don't know if my son would have reached 4'6" and if he doesn't continue it's likely that he'd develop obesity and other complications as growth hormone is responsible for more than height.
As far as it being a lifetime condition, it's different than type 1 diabetes that needs treatment, with growth hormone most kids stop shots during latter puberty.