Every time I read in the Bible the word "ungodly," I have to tell my self, "That does not mean someone without God."
For some reason, the Greek word asebes got translated into English as ungodly instead of impious. But perhaps many of us have no idea what impious means either--it's not a word you are likely to run into in the newspaper.
Piety, godliness and eusebeia, all mean to live or act in a way that is pleasing to God. Therefore, to be ungodly is not to live in a way that pleases God. And while the Bible often uses absolute language (one is either godly or ungodly), the Church teaches us that godliness is actually something we grow in. Therefore, even as we are growing in godliness, we have not yet quite left all ungodliness behind. St. Paul's exhortations to the Churches often include warnings to flee ungodliness. It's a process.
It's a transformation.