20/20 correctable means wearing glasses or contacts.
The term lazy eye can be a very vague term. The quick answer would be that if your son can correct to 20/20 with glasses then most likely there will not be an issue.
The long answer would be if he corrects to 20/20, and his refractive error (the strength of his prescription) is not over a certain limit, and if the refractive error difference between his right and left eye does not exceed a certain limit then there should not be an issue.
So, the best answer I can tell you right now, is that if your son is interested in the USCGA (or any other academy or ROTC program), he should apply and go through the medical process. That will be the only way to definitively give you an answer.
I hope this helps, and just know that when your son has completed his DoDMERB exam, there are folks here who are willing to help.